07 Jan The standard deviations

MATH225 Statistical Reasoning for the Health Sciences

Week 5 Assignment Understanding Normal Distribution

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).

If necessary, round to three decimal places.

Suppose John types 72 words per minute in a typing test on Sunday. The z-score when x = 72 is $$ . The mean is $$

This z-score tells you that x = 72 is $$ standard deviations to the right of the mean.

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).

If necessary, round to three decimal places.

Suppose Rosetta scores 110 points in the game on Thursday. The z-score when x=110 is $$?2.714. The mean is $$148.

This z-score tells you that x=110 is $$2.714 standard deviations to the left of the mean.

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.

A figure consists of three curves along a horizontal axis, labeled Upper A, Upper B and Upper C. Curve Upper A is farthest to the left, curve Upper B is farthest to the right, and curve Upper C is tall and skinny.

A

B

C

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

A figure consists of two curves labeled Upper A and Upper B. The curve Upper A is tall and evenly spread out from the center and the curve Upper is B is shorter and more spread out than A.

A has the larger mean.

B has the larger mean.

The means of A and B are equal.

A has the larger standard deviation.

B has the larger standard deviation.

The standard deviations of A and B are equal.

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

A figure consists of two curves labeled Upper A and Upper B. Curve Upper A is evenly spread out from the center, and curve Upper B is farther to the right than A and more evenly spread out.

A has the larger mean.

B has the larger mean.

The means of A and B are equal.

A has the larger standard deviation.

B has the larger standard deviation.

The standard deviations of A and B are equal.

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

A normal bell curve labeled Upper A and a normal elongated curve labeled Upper B are centered at the same point. Normal curve Upper B is narrower and above normal curve Upper A.

A has the larger mean.

B has the larger mean.

The means of A and B are equal.

A has the larger standard deviation.

B has the larger standard deviation.

The standard deviations of A and B are equal.

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

The z-score when x=11 is $$ . The mean is $$.

This z-score tells you that x=11 is $$ standard deviation(s) to the ___ of the mean.

Question Suppose X?N(16.5,2), and x=18.5. Find and interpret the z-score of the standardized normal random variable.

The z-score when x=18.5 is $$. The mean is $$