[Top Answer] MATH225N – Week 5 Assignment – Understanding Normal Distribution

Description

Week 5: Normal Distribution

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Week 5 – Understanding Normal Distribution

Activity 1

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.

Answer

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Activity 2

Question

Gail averages 64 words per minute on a typing test with a standard deviation of 9.5 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.

Provide your answer below:

Suppose Gail types 89 words per minute in a typing test on Sunday. The z-score when x = 89 is …… The mean is …… This z-score tells you that x = 89 is   standard deviations to the ……. of the mean.

Answer

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Activity 3

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.

Answer

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Activity 4

Question

Annie averages 23 points per basketball game with a standard deviation of 4 points. Suppose Annie’s points per basketball game are normally distributed. Let X= the number of points per basketball game. Then X∼N (23,4).

Provide your answer below:

Ans:

Suppose Annie scores 34 points in the game on Sunday. The z-score when x=34 is …… The mean is ……This z-score tells you that x=34 is …. standard deviations to the …… of the mean.

Answer

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Activity 5

Question

Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers.

B has the larger mean.

A has the larger standard deviation.

Answer

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Activity 6

Question

Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers.

Answer

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Activity 7

Question

Lexie averages 149 points per bowling game with a standard deviation of 14 points. Suppose Lexie’s points per bowling game are normally distributed. Let X= the number of points per bowling game. Then X∼N(149,14).

Ans:

Suppose Lexie scores 186 points in the game on Tuesday.

The z-score can be found using this formula:

…………..

Hence, the z-score when x = 186 is ……… The mean is ………. This z-score tells you that x = 186 is ……….. standard deviations to the ……… of the mean.

Answer

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Activity 8

Question

Suppose X∼N (12.5,1.5), and x=11. Find and interpret the z-score of the standardized normal random variable.

Answer

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Activity 9

Question

Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers.

Answer

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Activity 10

Question

Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers.

Answer

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Activity 11

Question

Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers.

Answer

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Activity 12

Question

Rosetta averages 148 points per bowling game with a standard deviation of 14 points. Suppose Rosetta’s points per bowling game are normally distributed. Let X= the number of points per bowling game. Then X∼N (148,14).

Answer

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Activity 13

Question

Suppose X∼N (16.5,0.5), and x=16. Find and interpret the z-score of the standardized normal random variable.

Answer

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Activity 14

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 normally distributed. Let X= the number of words per minute on a typing test. Then X∼N(58,11).

Answer

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