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Chapter 2: Q 3.3. (page 98)

Now suppose that you convert the class鈥檚 heights to z-scores. What would be the shape, center, and spread of this distribution? Explain.

Short Answer

Expert verified

Mean will become 0 (zero) and standard deviation would be 1 (one)

Step by step solution

01

Step 1. Given

02

Step 2. Concept

The following Minitab computer output validates the outcome: When each observation in distribution is standardized, the resultant set of z-scores has a mean of 0 and a standard deviation of 1

03

Step 3. Explanation

Height is now measured in z-scores. The shape will not be modified by the transformation from height to z-scores, therefore the shape will not be changed, but the mean will be shifted to 0 (zero) and the standard deviation will become1based on the given data (one)

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Most popular questions from this chapter

Use Table A to 铿乶d the proportion of observations from the standard Normal distribution that satis铿乪s each of the following statements. In each case, sketch a standard Normal curve and shade the area under the curve that is the answer to the question. Use your calculator or the Normal Curve applet to check your answers.

More Table A practice

(a) zis between 鈭�1.33and 1.65

(b) zis between 0.50and1.79

Estimating SD The figure at top right shows two Normal curves, both with mean 0. Approximately what is the standard deviation of each of these curves?

Normal is only approximate: ACT scores Scores on the ACT test for the 2007 high school graduating class had mean 21.2and standard deviation 5.0. In all, 1,300,599students in this class took the test. Of these, 149,164had scores higher than 27and another 50,310had scores exactly 27. ACT scores are always whole numbers. The exactly Normal N(21.2,5.0)distribution can include any value, not just whole numbers. What鈥檚 more, there is no area exactly above 27under the smooth Normal curve. So ACT scores can be only approximately Normal. To illustrate this fact, find

(a) the percent of 2007ACT scores greater than 27.

(b) the percent of 2007ACT scores greater than or equal to 27.

(c) the percent of observations from theN(21.2,5.0) distribution that are greater than 27. (The percent greater than or equal to 27 is the same, because there is no area exactly over 27.)

Blood pressure Larry came home very excited after a visit to his doctor. He announced proudly to his wife, 鈥淢y doctor says my blood pressure is at the 90thpercentile among men like me. That means I鈥檓 better off than about 90% of similar men.鈥� How should his wife, who is a statistician, respond to Larry鈥檚 statement?

3. What percent of young women have heights between 62 and 72 inches? Show your work.
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