MATH 225N Week 5 Assignment Understanding Normal Distribution

MATH 225N Week 5 Assignment: Understanding Normal Distribution

1. Question: John averages 58 words per minute on a typing test with a standard deviation of 11words per minute. Suppose John’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 (58,11).
2. 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 largest standard deviation.
3. Question: Isabella averages 152 points per bowling game with a standard deviation of 14.5points. Suppose Isabella’s points per bowling game are normally distributed. Let X= the number of points per bowling game. Then X∼N (152,14.5).
4. 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 standard deviation.
5. Question: Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers.
6. Question: Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers.
7. Question: Rosetta averages 148 points per bowling game with a standard deviation of 14points. Suppose Rosetta’s points per bowling game are normally distributed. Let X= the number of points per bowling game. Then X∼N (148,14).
8. 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 Assignment: Understanding Normal Distribution

1. 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.
2. 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 standard deviation.
3. Question: Suppose X∼N(18,2), and x=22. Find and interpret the z-score of the standardized normal random variable.
4. 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 standard deviation.
5. 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
6. 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 standard deviation
7. 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.
8. Question: Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers.
9. 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 largest standard deviation. 
10. Question: Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers.  
11. 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 largest standard deviation.  
12. 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.
13. Question: Which of the following lists of data has the smallest standard deviation? Select the correct answer below:
14. Question: Which of the following lists of data has the smallest standard deviation? Select the correct answer below:
15. Question: Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers.
16. Question: Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers. 
17. 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 largest mean. 
18. Question: Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers.  
19. Question: Suppose X∼N(5,1.5), and x=11. Find and interpret the z-score of the … normal random variable.
20. 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).
21. Question: Suppose X∼N(17,6), and x=5. Find and interpret the z-score of the … normal random variable.
22. 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).
23. Question: Suppose X∼N(5,2), and x=7.5. Find and interpret the z-score of the standardized normal random variable
24. 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). 
25. Question: Suppose X∼N(10,5), and x=11.5. Find and interpret the z-score of the … normal random variable.
26. 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).
27. Question: Suppose X∼N(9,5), and x=13.5. Find and interpret the z-score of the … normal random variable.
28. 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.
29. 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.
30. 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.
31. 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.
32. Question: Suppose X∼N(5,1.5), and x=9. Find and interpret the z-score of the … normal random variable.
33. Question: Suppose X∼N(16.5,0.5), and x=16. Find and interpret the z-score of the … normal random variable.
    

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MATH 225N Week 5 Assignment: Understanding Normal Distribution

1. 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).
2. Question: Suppose X∼N(18,2), and x=22. Find and interpret the z-score of the … normal random variable.
3. Question: Suppose X∼N(5,1.5), and x=11. Find and interpret the z-score of the … normal random variable.
4. 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).
5. Question: Suppose X∼N(5,1.5), and x=9. Find and interpret the z-score of the … normal random variable
6. Question: Suppose X∼N(10,5), and x=11.5. Find and interpret the z-score of the … normal random variable.
7. 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).
8. Question: Suppose X∼N(9,5), and x=13.5. Find and interpret the z-score of the standardized normal random variable.
9. 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).
10. Question: Suppose X∼N(5,2), and x=7.5.
11. 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). 
12. 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).
13. Question: Suppose X∼N(5,0.5), and x=16.
14. 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).
15. 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).
16. 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).
17. 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 … normal random variable.
18. Question: Suppose X∼N(5,2), and x=18.5.
19. Question: Suppose X∼N(5,1.5), and x=3.5.
20. Question: Suppose X∼N(20,2), and x=26.
21. 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).
    

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MATH 225N Week 5 Assignment: Understanding the Empirical Rule

1. 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.
2. 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?
3. 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?
4. 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?
5. 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.
6. 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.
7. 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? 
8. 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.
9. 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? 
10. Question: Suppose a random sample of monthly temperatures in a … 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?
11. 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.
    

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MATH 225N Week 5 Problems with Screenshots

1. 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?
2. Question: After collecting the data, Peter finds that the … test scores of the students in a school are normally … 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 … to two decimal places.
3. 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.