## MATH 225N Week 5 Assignment: Understanding Normal distribution

##### MATH 225N Week 5 Understanding Normal Distribution (From the Video)

**Question:**In2014, the CDC estimated that the mean height for adult women in the U.S. was 64 inches with a standard deviation of 4 Suppose X, height in inches of adult women, follows a normal distribution. Let x=68, the height of a woman who is 5′ 8″ tall. Find and interpret the z-score of the standardized normal random variable.**Question:**The graph below shows the graphs of several normal distributions, labeledA, B, and C, on the same axis. Determine which normal distribution has the smalleststandard deviation.**Question:**SupposeX∼N(18,2), and x=22. Find and interpret the z-score of the standardized normal random variable.**Question:**The graph below shows the graphs of several normal distributions, labeledA, B, and C, on the same axis. Determine which normal distribution has the smallest standard deviation.**Question:**The graph below shows the graphs of several normal distributions, labeledA, B, and C, on the same axis. Determine which normal distribution has the smallest mean**Question:**The graph below shows the graphs of several normal distributions, labeledA, B, and C, on the same axis. Determine which normal distribution has the smalleststandard deviation**Question:**The graph below shows the graphs of several normal distributions, labeledA, B, and C, on the same axis. Determine which normal distribution has the smallest mean.**Question:**Given the plot of normal distributionsA and B below, which of the following statements is true? Select all correct answers.**Question:**The graph below shows the graphs of several normal distributions, labeledA, B, and C, on the same axis. Determine which normal distribution has the largest standard deviation.**Question:**Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers.**Question:**The graph below shows the graphs of several normal distributions, labeledA, B, and C, on the same axis. Determine which normal distribution has the largest standard deviation.**Question:**The graph below shows the graphs of several normal distributions, labeled A, B, and C, on the same axis. Determine which normal distribution has the smallest mean.**Question:**Which of the following lists of data has the smallest standard deviation? Select the correct answer below:**Question:**Which of the following lists of data has the smallest standard deviation? Select the correct answer below:**Question:**Given the plot of normal distributionsA and B below, which of the following statements is true? Select all correct answers.**Question:**Given the plot of normal distributionsA and B below, which of the following statements is true? Select all correct answers.**Question:**The graph below shows the graphs of several normal distributions, labeledA, B, and C, on the same axis. Determine which normal distribution has the largest mean.**Question:**Given the plot of normal distributionsA and B below, which of the following statements is true? Select all correct answers.**Question:**SupposeX∼N(5,1.5), and x=11. Find and interpret the z-score of the standardized normal random variable.**Question:**Isabella averages17 points per basketball game with a standard deviation of 4 Suppose Isabella’s points per basketball game are normally distributed. Let X= the number of points per basketball game. Then X∼N(17,4).**Question:**Suppose X∼N(17,6), and x=5. Find and interpret the z-score of the standardized normal random variable.**Question:**The mean height of teenage males from Chile is 170 cm with a standard deviation of 28 cm. Male heights are known to follow a normal distribution. Let X = the height of a teenage male from Chile. Then X∼N(170,6.28).**Question:**SupposeX∼N(5,2), and x=7.5. Find and interpret the z-score of the standardized normal random variable**Question:**Jerome averages16 points a game with a standard deviation of 4 Suppose Jerome’s points per game are normally distributed. Let X = the number of points per game. Then X∼N(16,4).**Question:**SupposeX∼N(10,5), and x=11.5. Find and interpret the z-score of the standardized normal random variable.**Question:**Annie averages23 points per basketball game with a standard deviation of 4 Suppose Annie’s points per basketball game are normally distributed. Let X= the number of points per basketball game. Then X∼N(23,4).**Question:**SupposeX∼N(9,5), and x=13.5. Find and interpret the z-score of the standardized normal random variable.**Question:**In2014, the CDC estimated that the mean height for adult women in the U.S. was 64 inches with a standard deviation of 4 Suppose X, height in inches of adult women, follows a normal distribution. Let x=68, the height of a woman who is 5′ 8″ tall. Find and interpret the z-score of the standardized normal random variable.**Question:**Rosetta averages148 points per bowling game with a standard deviation of 14 Suppose Rosetta’s points per bowling game are normally distributed. Let X= the number of points per bowling game. Then X∼N(148,14). If necessary, round to three decimal places.**Question:**Gail averages64 words per minute on a typing test with a standard deviation of 5 words per minute. Suppose Gail’s words per minute on a typing test are normally distributed. Let X= the number of words per minute on a typing test. Then X∼N(64,9.5). If necessary, round to three decimal places.**Question:**William averages58 words per minute on a typing test with a standard deviation of 5 words per minute. Suppose William’s words per minute on a typing test are normally distributed. Let X= the number of words per minute on a typing test. Then X∼N(58,10.5).If necessary, round to three decimal places.**Question:**SupposeX∼N(5,1.5), and x=9. Find and interpret the z-score of the standardized normal random variable.**Question:**Suppose X∼N(16.5,0.5), and x=16. Find and interpret the z-score of the standardized normal random variable.

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##### MATH 225N Week 5 Understanding Normal Distribution

**Question:**Lexie averages 149 points per bowling game with a standard deviation of 14 Suppose Lexie’s points per bowling game are … Let*X*= the number of points per bowling game. Then*X*∼*N*(149,14).**Question:**Suppose*X*∼*N*(18,2), and*x*=22. Find and interpret the*z*-score of the standardized normal random variable.**Question:**Suppose*X*∼*N*(5,1.5), and*x*=11. Find and interpret the*z*-score of the standardized normal random variable.- Isabella averages 17 points per basketball game with a standard deviation of 4 Suppose Isabella’s points per basketball game are … Let
*X*= the number of points per basketball game. Then*X*∼*N*(17,4). **Question:**Suppose*X*∼*N*(5,1.5), and*x*=9. Find and interpret the*z*-score of the standardized normal random variable**Question:**Suppose*X*∼*N*(10,5), and*x*=11.5. Find and interpret the*z*-score of the standardized normal random variable.**Question:**Annie averages 23 points per basketball game with a standard deviation of 4 Suppose Annie’s points per basketball game are … Let*X*= the number of points per basketball game. Then*X*∼*N*(23,4).**Question:**Suppose*X*∼*N*(9,5), and*x*=13.5. Find and interpret the*z*-score of the standardized normal random variable.**Question:**Rosetta averages 148 points per bowling game with a standard deviation of 14 Suppose Rosetta’s points per bowling game are … Let*X*= the number of points per bowling game. Then*X*∼*N*(148,14).**Question:**Suppose*X*∼*N*(5,2), and*x*=7.5.**Question:**Jerome averages 16 points a game with a standard deviation of 4 Suppose Jerome’s points per game are normally distributed. Let*X*= the number of points per game. Then*X*∼*N*(16,4).**Question:**John averages 58 words per minute on a typing test with a standard deviation of 11 words per minute. Suppose John’s words per minute on a typing test are … Let*X*= the number of words per minute on a typing test. Then*X*∼*N*(58,11).**Question:**Suppose*X*∼*N*(5,0.5), and*x*=16.**Question:**Gail averages 64 words per minute on a typing test with a standard deviation of 5 words per minute. Suppose Gail’s words per minute on a typing test are … Let*X*= the number of words per minute on a typing test. Then*X*∼*N*(64,9.5).**Question:**William averages 58 words per minute on a typing test with a standard deviation of 5 words per minute. Suppose William’s words per minute on a typing test are … Let*X*= the number of words per minute on a typing test. Then*X*∼*N*(58,10.5).**Question:**Hugo averages 22 points per basketball game with a standard deviation of 4 Suppose Hugo’s points per basketball game are normally distributed. Let*X*= the number of points per basketball game. Then*X*∼*N*(22,4).**Question:**In 2014, the CDC estimated that the mean height for adult women in the U.S. was 64 inches with a standard deviation of 4 Suppose*X*, height in inches of adult women, follows a normal distribution. Let*x*=68, the height of a woman who is 5′ 8″ tall. Find and interpret the*z*-score of the standardized normal random variable.**Question:**Suppose*X*∼*N*(5,2), and*x*=18.5.**Question:**Suppose*X*∼*N*(5,1.5), and*x*=3.5.**Question:**Suppose*X*∼*N*(20,2), and*x*=26.**Question:**Isabella averages 152 points per bowling game with a standard deviation of 5 points. Suppose Isabella’s points per bowling game are … Let*X*= the number of points per bowling game. Then*X*∼*N*(152,14.5).

##### MATH 225N Week 5 Understanding the Empirical Rule

**Question:**A random sample of CO2 levels in a school has a sample mean of*x*¯=4 ppm and sample standard deviation of*s*=86.7 ppm. Use the Empirical Rule to determine the approximate percentage of CO2 levels that lie between 338.3 and 858.5 ppm.**Question:**Suppose that a random sample of redwood trees has a sample mean diameter of*x*¯=1 feet, with a sample standard deviation of*s*=3.7 feet. Since the diameters of redwood trees are generally symmetric and bell-shaped, we can apply the Empirical Rule. Between what two diameters are approximately 68% of the data?**Question:**Suppose a random sample of monthly rainfalls in a given area has a sample mean of*x*¯=2 inches, with a sample standard deviation of*s*=3.5 inches. Since rainfall amounts in this area are generally symmetric and bell-shaped, we can apply the Empirical Rule. Between what two amounts are approximately 99.7% of the data?**Question:**Suppose a random sample of adult women has a sample mean height of*x*¯=3 inches, with a sample standard deviation of*s*=2.4 inches. Since height distribution are generally symmetric and bell-shaped, we can apply the Empirical Rule. Between what two heights are approximately 99.7% of the data?**Question:**For the same random sample of adult women, with a sample mean height of*x*¯=3 inches and sample standard deviation of*s*=2.4inches, use the Empirical Rule to determine the approximate percent of heights that lie between 59.5 inches and 69.1 inches.**Question:**Returning to the sample of adult women, with a sample mean height of*x*¯=3 inches and sample standard deviation of*s*=2.4 inches, use the Empirical Rule to estimate the percentage of heights that are less than 61.9 inches.**Question:**A random sample of males has a sample mean blood volume of*x*¯=2 liters, with a sample standard deviation of*s*=0.2 liters. Since blood volumes in males are generally symmetric and bell-shaped, we can apply the Empirical Rule. Between what two volumes are approximately 95% of the data?**Question:**A random sample of men’s weights have a sample mean of*x*¯=3 pounds and sample standard deviation of*s*=12.7 pounds. Use the Empirical Rule to determine the approximate percentage of men’s weights that lie between 156.9 and 207.7 pounds.**Question:**A random sample of waiting times at a bus stop has a sample mean time of*x*¯=6 seconds, with a sample standard deviation of*s*=29.4 seconds. Since waiting times at this bus stop are generally symmetric and bell-shaped, we can apply the Empirical Rule. Between what two waiting times are approximately 95% of the data?**Question:**Suppose a random sample of monthly temperatures in a given area has a sample mean of*x*¯=2∘*F*, with a sample standard deviation of*s*=1.5∘*F*. Since temperatures in this area are generally symmetric and bell-shaped, we can apply the Empirical Rule. Between what two temperatures are approximately 99.7% of the data?**Question:**A random sample of small business stock prices has a sample mean of*x*¯=$82 and sample standard deviation of*s*=$8.95. Use the Empirical Rule to estimate the percentage of small business stock prices that are more than $81.

##### MATH 225N Week 5 Problems with Screenshots

**Question:**A data set has mean of 4 and standard Deviation of 4. What is the probability that a randomly … data value is greater than 78?**Question:**After collecting the data, Peter finds that the standardized test scores of the students in a school are normally distributed with mean 85 points and standard deviation 3 points. Use the Empirical Rule to find the probability that a randomly … student’s score is greater than 76 points. Provide the final answer as per percent rounded to two decimal places.**Question:**Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers….. The means of A and B are equal….. B has the larger standard deviation.