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Chapter 2: Q. 2.1 (page 119)

Use Table A in the back of the book to find the proportion of observations from a standard Normal distribution that fall in each of the following regions. In each case, sketch a standard Normal curve and shade the area representing the region.

z<1.39

Short Answer

Expert verified

The standard Normal curve, with the region represented by the area, is as follows:

Step by step solution

01

Given Information 

Z-score : z<1.39

02

Explanation 

From Table A:

P(z<1.39)=0.9177

The graphical representation is:

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Most popular questions from this chapter

Use Table A to find the proportion of observations from the standard Normal distribution that satisfies 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 −2.05and 0.78

(b) zis between −1.11and −0.32

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’s 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.)

Paul is15years old and 179cm tall.

(a) Find the z-score corresponding to Paul’s height. Explain what this value means.

(b) Paul’s height puts him at the85th percentile among 15-year-old males. Explain what this means to someone who knows no statistics.

A Normal curve Estimate the mean and standard deviation of the Normal density curve in the figure below:
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