Approximately normal distribution formula. 2: A Single Population Mean using the Normal Distribution.

67448σ Q 1 = μ − 0. Its distribution is the standard normal, Z ~N(0, 1). Using this information, answer the following questions (round answers to one decimal place). The graph below shows examples of Poisson distributions with Oct 2, 2020 · Approximate the expected number of days in a year that the company produces more than 10,200 chips in a day. 1 is a special case of what is called the binomial distribution. 55) 15. Look at the histograms of lifetimes given in Figure 21. 13. This is true if our parent population is normal or if our sample is reasonably large ( n ≥ 30) ‍. In mathematical notation, the five-number summary for the normal distribution with mean and standard deviation is as follows: Five-Number Summary for a Normal Distribution. The conditions we need for inference on a mean are: Random: A random sample or randomized experiment should be used to obtain the data. Your textbook uses an abbreviated form of this, known as the 95% Rule, because 95% is the most commonly used interval. Step 2: A weight of 35 lbs is one standard deviation above the mean. The Gaussian (normal) approximation. In statistics, the 68–95–99. 3, σ = 7. While the sampling distribution of the mean is the most common type, they can characterize other statistics, such as the median, standard deviation, range, correlation, and test statistics in hypothesis tests. 7 rule, or empirical rule, which you can see in the image below. 99. These measures are useful for understanding the distribution's center and spread, respectively, regardless of its shape. For the USA: So for the USA, the lower and upper bounds of the 95% confidence interval are 34. Compute the following probability: Solution. The symmetric, unimodal, bell curve is ubiquitous throughout statistics. height, weight, etc. Example 16-1. where μ μ = mean of the population of the x value and σ σ = standard deviation for the population of the x value. 7% of the normally distributed data respectively. Randomization: The data must be sampled randomly such that every member in a population has an equal probability of being selected to be in the sample. The y -axis contains the probability of x, where X = the number of workers who have only a high school diploma. The distribution of the protein content in cow's milk has the classic bell shape of the normal distribution. This value for the total area corresponds to 100 percent. Find the probability that the sample proportion computed from a sample of size \(900\) will be within \(5\) percentage points of the true population proportion. It represents a distribution of standardized scores, called z-scores, as opposed to raw scores (the actual data values). This term means that when we integrate the function to find the area under the curve, the entire area under the curve is 1. 5. Use your calculator, a computer, or a probability table for the standard normal distribution to find z 0. 35). Poisson Approximation To Normal – Example. Jan 31, 2022 · Sampling distributions describe the assortment of values for all manner of sample statistics. Normal Distribution Problems and Solutions. If you scored an 80%: Z = ( 80 − 68. Since the mean for the standard normal distribution is zero and the standard deviation is one, then the transformation in Equation \ref{zscore} produces the distribution \(Z \sim N(0, 1)\). Note: For this standard deviation formula to be accurate, our sample size needs to be 10 % or less of the population so we can assume independence. Thanks to the central limit theorem, you can count on the approximation if you have a large sample (say at least 50 data points) and treat your distribution as normal. 02 and 35. Jan 21, 2021 · To convert from a normally distributed x value to a z-score, you use the following formula. The sampling distribution for a sample proportion will be normally distributed when: Population size (N) is at least 10 times sample size (n). 7% of the population is within 3 standard deviation of the mean. Due to its shape, it is often referred to as the bell curve: Owing largely to the central limit theorem, the normal distributions is an appropriate approximation even when the underlying In order to estimate the sample size, we need approximate values of p 1 and p 2. The sampling method is simple random sampling . But \ (p\) is not known. That is, you are given the percentage or statistical probability of being at or below a certain x-value, and you have to find the x-value that corresponds to it. [2] [3] 若 隨機變數 服從一個 Use this calculator to easily calculate the p-value corresponding to the area under a normal curve below or above a given raw score or Z score, or the area between or outside two standard scores. Suppose that our sample has a mean of x - x - = 10, and we have constructed the 90% confidence interval (5, 15) where EBM = 5. The formula for the variance is σ 2 = npq. In the United States the ages 13 to 55+ of smartphone users approximately follow a normal distribution with approximate mean and standard deviation of 36. So, the calculation of Z-score can be done as follows-. A normal distribution formula calculation follows a bell curve. 9 years, respectively. 3. The binomial distribution describes the probability of having exactly k successes in n independent Bernoulli trials with probability of a success p (in Example 5. Normal: The sampling distribution of x ¯. X ~ U(a, b) where a = the lowest value of x and b = the highest value of x. The t -distribution, also known as Student’s t -distribution, is a way of describing data that follow a bell curve when plotted on a graph, with the greatest number of observations close to the mean and fewer observations in the tails. A Z distribution may be described as N ( 0, 1). Example 6. Figure 4. The reading speed of second-grade students in a large city is approximately normal, with a mean of 89 words per minute (wpm) and a standard deviation of 10 wpm. Suppose that our sample has a mean of [latex]\displaystyle\overline{{x}}={10}[/latex] and we have constructed the 90% confidence interval (5, 15) where EBM = 5. The skew normal still has a normal-like tail in the direction of the skew, with a shorter tail in the other direction; that is, its density is asymptotically proportional to for some positive . Actually, the normal distribution is based on the function exp (-x²/2). Jan 18, 2024 · Input the population parameters in the sampling distribution calculator (μ = 161. 9962 \nonumber\] The Empirical Rule is a rule telling us about where an observation lies in a normal distribution. (c) The teacher wants to transform the test scores so that they have an approximately Normal distribution with a mean of 80 points and a standard deviation of 10 points. When n ≥ 30, the central limit theorem applies. A standard normal distribution has a mean of 0 and variance of 1. Let be a normal random variable with mean and variance . For normalization purposes. z = x − μ σ (6. That is, \ (X\sim N (100, 16^2)\). A distribution is approximately Normal when the Normal distribution can be used as an approximate distribution. Definition 6. Suppose \ (Y\) denotes the number of events occurring in an interval with mean \ (\lambda\) and variance \ (\lambda\). Constructing a Confidence Interval for the Population Proportion. 3 cm (b The exponentially modified normal distribution is another 3-parameter distribution that is a generalization of the normal distribution to skewed cases. Apr 23, 2022 · Wald's Equation. 99. The central limit theorem and the law of large numbers are the two fundamental theorems of probability. The z-score is three. Unpacking the meaning from that complex definition can be difficult. 1) Select left-tailed, in this case. 04 and 36. Suppose that our sample has a mean of [latex]\displaystyle\overline { {x}}= {10} [/latex] and we have constructed the 90% confidence interval (5, 15) where EBM = 5. Suppose that our sample has a mean of and we have constructed the 90% confidence interval (5, 15) where EBM = 5. Apr 23, 2022 · 3. To do this, she will use a formula in the form: new score = a + b (old score) Find the values of a and b that the teacher should use to transform the distribution of test scores. The probability that the sample mean age is more than 30 is given by: \ [P (Χ > 30) = \text {normalcdf} (30,E99,34,1. 01 and the area to the left is 0. 4 grams) but a few are much larger or smaller. The integral of the rest of the function is square root of 2xpi. In that case, the excess kurtosis of a normal distribution would be be 3 − 3 = 0. 7% of the values lie within one, two, and three standard deviations of the mean, respectively. 1: Normal Distribution. 1 standard deviation of the mean. 7 years old. Round your answers to one decimal place. Jan 13, 2020 · The square root term is present to normalize our formula. This is common when the number of samples or parts making up a distribution grows; for example, if you have 100 coin tosses the resulting Binomial distribution is, for most purposes, approximately Normal. Your result is ready. The 68-95-99 rule is based on the mean and standard deviation. You may see the notation N ( μ, σ 2) where N signifies that the distribution is normal, μ is the mean, and σ 2 is the variance. Sample size and standard deviations Mar 12, 2023 · A normal distribution with mean μ = 0 and standard deviation σ = 1 is called the standard normal distribution. In the text below, you'll find the definition of the empirical rule Binomial probability mass function and normal probability density function approximation for n = 6 and p = 0. The letter Z is used exclusively to denote a variable that has a standard normal distribution and is written Z ~ N(0, 1). The value \(x\) comes from a normal distribution with mean \(\mu\) and standard deviation \(\sigma\). Mar 14, 2024 · Normal Distribution Formula Explained. As the confidence level increases, the corresponding EBM increases as well. 01 having the property that the area under the normal density curve to the right of z 0. x = 3, μ = 4 and σ = 2. EBM = (To find the 98% confidence interval, find – EBM = 1. 95% Confidence Interval. With mean zero and standard deviation of one it functions as a standard normal distribution calculator (a. 7 - The Empirical Rule. = (940 – 850) / 100. Oct 3, 2018 · Step 1: Sketch a normal distribution with a mean of μ=30 lbs and a standard deviation of σ = 5 lbs. It gives the probability of an event happening a certain number of times ( k) within a given interval of time or space. The Empirical Rule, which is also known as the three-sigma rule or the 68-95-99. Z – score = ( X – µ ) / σ. 95% of the population is within 2 standard deviation of the mean. In probability theory, the central limit theorem ( CLT) states that, under appropriate conditions, the distribution of a normalized version of the sample mean converges to a standard normal distribution. The shape of the binomial distribution needs to be similar to the shape of the normal distribution. Jan 14, 2023 · 9. 5 can be used to generate the most conservative, or largest, sample sizes. 7% will occur within three standard deviations. 98. We would like to determine the probabilities I have a question about the usefulness of the Central Limit Theorem. k. Calculating the Confidence Interval The standard normal distribution is a normal distribution in which the mean (μ) is 0 and the standard deviation (σ) and variance (σ 2) are both 1. It is known as the bell curve as it takes the shape of the bell. Then the binomial distribution of a sample (estimated) proportion can be approximated by the normal distribution with μ = p μ = p The mean of the sampling distribution is always equal to the population proportion (p), and the standard deviation is calculated as sqrt (p (1 − p) / n), where n is the sample size. 74, which means your score of 80 was 0. 15% = 16%. If you try to graph that, you'll see Use a Z test when you need to compare group means. n * (1 - p) ≥ 10. Jan 6, 2022 · A normal distribution is the most commonly used distribution in all of statistics. 96. Suppose that our sample has a mean of \(\bar{x} = 10\) and we have constructed the 90% confidence interval (5, 15) where \(E = 5\). It is a type of normal distribution used for smaller sample sizes, where the The key takeaways from this lesson are summarized below. Suppose X ∼ N(5, 6) X ∼ N ( 5, 6). Most observations are near the mean (3. When graphing the data from each of the examples in the introduction, the distributions from each of these situations would be mound-shaped and mostly symmetric. Formula Review. 11. A particular value of Z is denoted z (lower-case) and is referred to as a z-score. Standard deviation = 2. Z Score = 0. May 10, 2022 · Revised on November 10, 2023. The Poisson distribution has only one parameter, λ (lambda), which is the mean number of events. Thus, if there is no information available to approximate p 1 and p 2, then 0. The mean of the z-scores is zero and the standard deviation is one. If n is large enough, then the skew of the distribution is not too great. Suppose that our sample has a mean of x ¯ x ¯ = 10, and we have constructed the 90% confidence interval (5, 15) where EBM = 5. ) A USE SALT (a) Calculate the value (in centimeters) representing the lowest 25% of diameters of cantaloupes. To calculate probabilities related to the normal distribution in Excel, you can use the NORMDIST function, which uses the following basic syntax: =NORMDIST(x, mean, standard_dev, cumulative) where: x: The value of interest in the normal distribution. Let X = length, in seconds, of an eight-week-old baby's smile. (the sample mean) needs to be approximately normal. Jan 18, 2024 · Use the normal approximation calculator to approximate the probability for a binomial event with a normal distribution. No matter what the population looks like, those sample means will be roughly normally distributed given a reasonably large sample size (at least 30). So, the normal distribution has kurtosis of 3, but its excess kurtosis Step 1. a. The unpaired t method tests the null hypothesis that the population means related to two independent, random samples from an approximately normal distribution are equal (Altman, 1991; Armitage and Berry, 1994). 5 days ago · The empirical rule calculator (also a 68 95 99 rule calculator) is a tool for finding the ranges that are 1 standard deviation, 2 standard deviations, and 3 standard deviations from the mean, in which you'll find 68, 95, and 99. Learning Outcomes. Apr 30, 2018 · In this blog post, learn how to use the normal distribution, about its parameters, the Empirical Rule, and how to calculate Z-scores to standardize your data and find probabilities. 7 rule, represents a high-level guide that can be used to estimate the proportion of a normal distribution that can be found within 1, 2, or 3 standard deviations of the mean. 9 years respectively. . z table calculator), but you can enter Jan 30, 2024 · In the United States the ages 13 to 55+ of smartphone users approximately follow a normal distribution with approximate mean and standard deviation of 36. By the formula of the probability density of normal distribution, we can write; Hence, f(3,4,2) = 1. A z-score is measured in units of the standard deviation. This function gives an unpaired two sample Student t test with a confidence interval for the difference between the means. Skewness is a measure of the asymmetry of a distribution. µ−2 σ µ−1 σ µ+1 σ µ−3 σ µ+3 σ µ µ+2 Jul 1, 2020 · In the United States the ages 13 to 55+ of smartphone users approximately follow a normal distribution with approximate mean and standard deviation of 36. Jan 29, 2021 · σ = √np (1-p) It turns out that if n is sufficiently large then we can actually use the normal distribution to approximate the probabilities related to the binomial distribution. The number of successes in n trials has the binomial (n, p) distribution. 67448 σ. 01 = 2. This is the main idea of the Central Mar 15, 2024 · Solution: Use the following data for the calculation of standard normal distribution. For a recent final exam in STAT 500, the mean was 68. A normal distribution is symmetrical and bell-shaped. A normal distribution is a perfectly …. The central limit theorem states that under certain (fairly common) conditions, the sum of many random variables will have an approximately normal distribution. To ensure this, the quantities np and nq must both be greater than five (n p > 5 n p > 5 and n q > 5 n q > 5 ). 024 – 0. 74 SD above the mean For example, in Lesson 2 we learned about the Empirical Rule which stated that approximately 68% of observations on a normal distribution will fall within one standard deviation of the mean, approximately 95% will fall within two standard deviations of the mean, and approximately 99. 7% will fall within three standard deviations of the mean. Jul 19, 2021 · A popular normal distribution problem involves finding percentiles for X. 395 days per year. n * p ≥ 10, where p is the sample proportion. 326. 45 = 0. A z-score indicates the number of standard deviation a score falls above or below the mean. Suppose the diameter of a cantaloupe can be modeled by an approximately normal distribution with a mean of 12 cm and a standard deviation of 1 cm. This is often helpful as many statistical tests rely on the data being Normally Aug 7, 2020 · To calculate the 95% confidence interval, we can simply plug the values into the formula. The normal curve showing the empirical rule. The calculation is as follows: x = μ + (z)(σ) = 5 + (3)(2) = 11. This random variable may be expressed Apr 2, 2023 · The confidence level is the percent of all possible samples that can be expected to include the true population parameter. Aug 7, 2020 · The 68-95-99 rule. A right-skewed distribution is longer on the right side of its peak, and a left-skewed Oct 11, 2023 · A normal distribution has a kurtosis of 3. Just as the Central Limit Theorem can be applied to the sum of independent Bernoulli random variables, it can be applied to the sum of independent Poisson random variables. 01 is 0. This says that x x is a normally distributed random variable with mean μ = 5 μ = 5 and standard deviation σ = 6 σ = 6. It should be 0. This simplifies the above probability density function to: Any normal distribution can be converted to a standard normal distribution, which is useful because a normal distribution can have any Part 2: Find the mean and standard deviation of the sampling distribution. 55 with a standard deviation of 15. 2. Jul 6, 2022 · The sampling distribution will follow a similar distribution to the population. The Empirical Rule is a statement about normal distributions. Roughly, the central limit theorem states that the distribution of the sum (or average) of a large number of independent, identically distributed variables will be approximately normal, regardless of the underlying distribution. Using this information, answer the following questions. \ (sample\;statistic \pm 2 (standard\;error)\) The 2 in this formula comes from the normal distribution. 7 rule, also known as the empirical rule, and sometimes abbreviated 3sr, is a shorthand used to remember the percentage of values that lie within an interval estimate in a normal distribution: approximately 68%, 95%, and 99. 1: The Normal Distribution is shared under a license and was authored, remixed, and/or curated by LibreTexts. Jan 18, 2024 · We use the Z-score if the test statistic approximately follows the standard normal distribution N(0,1). Mean = 4 and. Therefore, the sampling distribution will only be normal if the population is normal. 1, n = 4, k = 1, p = 0. 95% of values are within. Apr 2, 2023 · The central limit theorem states that for large sample sizes (\ (n\)), the sampling distribution will be approximately normal. By the central limit theorem, EBM = z σ √n. The Empirical Rule states that approximately 68% of data will be within one standard deviation of the mean, about 95% will be within two standard deviations of the mean, and about 99. Suppose that our sample has a mean of ˉx = 10, and we have constructed the 90% confidence interval (5, 15) where EBM = 5. Many practical distributions approximate to the normal distribution. 16 * 200 = 32. Jul 29, 2022 · Normal distribution is commonly associated with the 68-95-99. Aug 10, 2020 · The scenario outlined in Example 5. Indeed it is so common, that people often know it as the normal curve or normal distribution, shown in Figure \ (\PageIndex {1}\). I assume that in a real-world situation, you would create a probability distribution function based on the data you have from a specific sample The value x x comes from a normal distribution with mean μ μ and standard deviation σ σ. First of all, we need to express the above probability in terms of the distribution function of : Then, we need to express the distribution function of in terms of the distribution function of a standard normal random variable : Jan 19, 2021 · In order to apply the central limit theorem, there are four conditions that must be met: 1. Jul 1, 2020 · A confidence interval for a population mean with a known standard deviation is based on the fact that the sample means follow an approximately normal distribution. The normal distribution is very important because of the following points: 1. The histogram that could be constructed from the sample is an empirical distribution that closely matches the theoretical uniform distribution. Z Score obtained using standard normal distribution formula in Excel is –. One of the most important characteristics of a normal curve is that it is symmetric, which means one can divide the positive and negative values of the distribution into equal halves. 4. 5% + 2. 45. However, sometimes people use “excess kurtosis,” which subtracts 3 from the kurtosis of the distribution to compare it to a normal distribution. ‍. Check all conditions before using the sampling distribution of the sample proportion. It has long been known that \ (X\) follows a normal distribution with mean 100 and standard deviation of 16. Use the 1-sample analysis to determine whether a population mean is different from a hypothesized value. A distribution is asymmetrical when its left and right side are not mirror images. In this case a reasonable approximation to B(n, p) is given by the normal distribution (, ()), Aug 28, 2020 · Revised on June 21, 2023. I focus on the mean in this post. Q1 = μ − 0. A confidence interval for a population mean with a known standard deviation is based on the fact that the sample means follow an approximately normal distribution. 3. Input the sample data (n = 7, X = 160). This is known as the normal approximation to the binomial. For example, if you know that the people whose golf scores were in the lowest 10% got to go to a tournament Oct 29, 2018 · By Jim Frost105 Comments. 9 years and 13. The central limit theorem, referred to in the discussion of the Gaussian or normal distribution above, suggests that the binomial and Poisson distributions should be approximated by the Gaussian. ) and test scores. Or use the 2-sample version to determine whether two population means differ. The empirical rule in statistics, also known as the 68 95 99 rule, states that for normal distributions, 68% of observed data points will lie inside one standard deviation of the mean, 95% will fall within two standard deviations, and 99. Take a sample from a population, calculate the mean of that sample, put everything back, and do it over and over. 1431 The Empirical Rule is a rule telling us about where an observation lies in a normal distribution. The normal distribution, also called the Gaussian distribution, is a probability distribution commonly used to model phenomena such as physical characteristics (e. Solution: Given, variable, x = 3. Z ~ N(0, 1) z = a standardized value (z In the United States the ages 13 to 55+ of smartphone users approximately follow a normal distribution with approximate mean and standard deviation of 36. 4%. 1) (6. The notation for the uniform distribution is. med = μ m e d = μ. There are several versions of the CLT, each applying in the Sampling distribution of the sample mean. 2. 1 6. 314039. 2 standard deviations of the mean. This means that if the probability of producing 10,200 chips is 0. 正态分布 （ normal distribution ，台湾作 常態分布 ），物理学中通称 高斯分佈 （ Gaussian distribution ） [1] ，是一個非常常見的 連續機率分布 。. Determine the probability that a random smartphone user in the age range 13 to 55+ is between 23 and 64. To get a 90% confidence interval, we must include the May 13, 2022 · A Poisson distribution is a discrete probability distribution. 7 percent of the data is within three standard deviations (σ) of the mean (μ). If zis the z-score for a value x from the normal distribution N(µ, σ) then z tells you how many standard deviations x is above (greater than) or below (less than) µ. A distribution can have right (or positive), left (or negative), or zero skewness. 2: A Single Population Mean using the Normal Distribution. To construct a confidence interval we're going to use the following 3 steps: CHECK CONDITIONS. 2 - Normal Approximation to Poisson. Independence: The sample values must be independent of each other. min = μ − 3σ m i n = μ − 3 σ. Question A (Part 2) 2. 1) z = x − μ σ. As the sample size increases, the EBM decreases. According to the 95% Rule, approximately 95% of a normal distribution falls within 2 standard deviations of the mean. To find the z-score for a particular observation we apply the following formula: Let's take a look at the idea of a z-score within context. Therefore, the probability that the average height of those women falls below 160 cm is about 31. The 'standard normal' is an important distribution. This formula is used for calculating probabilities that are related to a normal distribution. Sixty-eight percent of the data is within one standard deviation (σ) of the mean (μ), 95 percent of the data is within two standard deviations (σ) of the mean (μ), and 99. 023, we would expect this to happen approximately 365 (0. 90. (Use a table or SALT. 1: z-score. Mar 26, 2023 · Verify that the sample proportion \(\hat{p}\) computed from samples of size \(900\) meets the condition that its sampling distribution be approximately normal. 41) = 8. 106. The sampling distribution will approximately follow a normal distribution. The Standard Deviation is a measure of how spread out numbers are (read that page for details on how to calculate it). Add the percentages above that point in the normal distribution. The normal distribution is a good model for measurements of many kinds, including IQs, heights, and lengths of pregnancies. A confidence interval for a population mean, when the population standard deviation is known based on the conclusion of the Central Limit Theorem that the sampling distribution of the sample means follow an approximately normal distribution. g. This is also known as a z distribution. So it must be normalized (integral of negative to positive infinity must be equal to 1 in order to define a probability density distribution). A confidence interval for a population mean with a known standard deviation is based on the fact that the sampling distribution of the sample means follow an approximately normal distribution. We previously used \ (np\) and \ (n (1-p)\). All of these together give the five-number summary. Chapter 8. For example, if the mean of a normal distribution is five and the standard deviation is two, the value 11 is three standard deviations above (or to the right of) the mean. The 95% Rule states that approximately 95% of observations fall within two standard For example, if the mean of a normal distribution is five and the standard deviation is two, the value 11 is three standard deviations above (or to the right of) the mean. 1. 023) = 8. For GB: So for the GB, the lower and upper bounds of the 95% confidence interval are 33. 5) = 0. Complete parts (a) What is the probability a randomly selected student in the city will read more than 95 words per m The standardized normal distribution is a type of normal distribution, with a mean of 0 and standard deviation of 1. The mean for the standard normal distribution is zero, and the standard deviation is one. Thanks to the empirical rule, the mean and standard Jan 17, 2021 · You need to find z 0. Let \ (X\) denote the IQ (as determined by the Stanford-Binet Intelligence Quotient Test) of a randomly selected American. When we calculate the standard deviation we find that generally: 68% of values are within. It says: 68% of the population is within 1 standard deviation of the mean. A Z test is a form of inferential statistics. This holds even if the original variables themselves are not normally distributed. For n to be “sufficiently large” it needs to meet the following criteria: np ≥ 5. 7% will be within three standard deviations of the mean. It uses samples to draw conclusions about populations. The sampling distribution of a sample proportion p ^ has: μ p ^ = p σ p ^ = p ( 1 − p) n. The values of p 1 and p 2 that maximize the sample size are p 1 =p 2 =0. The central limit theorem in statisticsstates that, given a sufficiently large samplesize, the sampling distribution of the mean for a variable will approximate a normal distribution regardless of that variable’s distribution in the population. 4 and you will see that they resemble the normal distribution. —Round answers to one decimal place. 3 and of resistances given in Figure 21. Step 3: Since there are 200 otters in the colony, 16% of 200 = 0. Among all the distributions we see in practice, one is overwhelmingly the most common. 常態分布在 统计学 上十分重要，經常用在 自然 和 社会科学 來代表一個不明的隨機變量。. 35% + 0. The number of adult workers that you expect to have a high school diploma but not pursue any further education is the mean, μ = np = (20) (0. 1. In this video, the normal distribution curve produced by the Central Limit Theorem is based on the probability distribution function. 28. n (1-p) ≥ 5. Question 1: Calculate the probability density function of normal distribution using the following data. gv dx hf dm mu mk md hr by dk