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Chapter 2: Q 2.1. (page 91)

Lynette, a student in the class, is 65 inches tall. Find and interpret her z-score.

Short Answer

Expert verified

z−score is the−0.466.

Step by step solution

01

Step 1. Given

A dot plot shows the height distribution in the class, as well as summary data from the computer output.

02

Step 2. Concept

Value that has been standardized (z-score) The standardized value of xis z=x-meanstandarddeviationif xis an observation from a distribution with known mean and standard deviation. A z-score is a term used to describe a standardized value.

03

Step 3. Explanation

If xis an observation from a distribution that has known mean and standard deviation, standardized score forxis,

z=x−meanstandarddeviation

So here, x=65

And from the given dot plot x=67and standard deviation is Sx=4.09

z=65-674.29

z=-0.466

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Most popular questions from this chapter

Use Table A to find the value zfrom the standard Normal distribution that satisfies 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.

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

(a) 0

(b) 1

(c) 2

(d) 4

(e) 5

About what percent of the cockroaches have weights less than 78 grams?

(a) 34%

(b) 32%

(c) 16%

(d) 2.5%

(e) none of these

Weights aren’t Normal The heights of people of the same gender and similar ages follow Normal distributions reasonably closely. Weights, on the other hand, are not Normally distributed. The weights of women aged 20 to 29 have mean 141.7 pounds and median 133.2 pounds. The first and third quartiles are 118.3 pounds and 157.3 pounds. What can you say about the shape of the weight distribution? Why?
Now suppose that you convert the class’s heights to z-scores. What would be the shape, center, and spread of this distribution? Explain.
See all solutions

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