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.
