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Chapter 2: Q. 2 (page 138)

T2.2. For the Normal distribution shown, the standard deviation is closest to

(a) 0

(b) 1

(c) 2

(d) 4

(e) 5

Short Answer

Expert verified

Option (d) 4

Step by step solution

01

Concept Introduction (Part a)

Standard deviation describes how far values vary from the mean of the set, while a high standard deviation indicates a more wide-ranging variation. A low standard deviation indicates closeness to the mean, while a high standard deviation indicates the values are spread out over a larger range.

02

Explanation 

We observe that the normal distribution peak is at about 4. This means that the mean is at the peak of the normal distribution.

渭鈮�4

This distance from 渭=4to inflection point (where the curve appears approximately straight) is the standard deviation of the normal distribution.

Therefore, the standard deviation in this case is 4 (i.e.). In this case, the distance is about 4 and the standard deviation is approximately 4.

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Most popular questions from this chapter

Density curves Sketch a density curve that might describe a distribution that has a single peak and is skewed to the left.

Now mark the approximate location of the mean. Explain why the mean and median have the relationship that they do in this case.

Comparing bone density Refer to the previous exercise. One of Judy鈥檚 friends, Mary, has the bone density in her hip measured using DEXA. Mary is 35 years old. Her bone density is also reported as 948g/cm2, but her standardized score isz=0.50. The mean bone density in the hip for the reference population of 35-year-old women is 944grams/cm2.

(a) Whose bones are healthier鈥擩udy鈥檚 or Mary鈥檚? Justify your answer.

(b) Calculate the standard deviation of the bone density in Mary鈥檚 reference population. How does

this compare with your answer to Exercise 13(b)? Are you surprised?

Use Table A to 铿乶d the value zfrom the standard Normal distribution that satis铿乪s each of the following conditions. In each case, sketch a standard Normal curve with your value of zmarked on the axis. Use your calculator or the Normal Curve applet to check your answers.

Working backward

(a) The 10th percentile.

(b) 34% of all observations are greater thanz.

T2.1. Many professional schools require applicants to take a standardized test. Suppose that 1000 students take such a test. Several weeks after the test, Pete receives his score report: he got a 63, which placed him at the 73rd percentile. This means that

(a) Pete's score was below the median.

(b) Pete did worse than about 63%of the test takers.

(c) Pete did worse than about 73%of the test takers.

(d) Pete did better than about 63%of the test takers.

(e) Pete did better than about 73%of the test takers.
See all solutions

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