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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鈭�score is the鈭�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鈭�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 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 63rd percentile.

(b) 75% of all observations are greater than z.

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R2.8 Working backward

(a) Find the number zat the 80th percentile of a standard Normal distribution.

(b) Find the number localid="1649404103275" zsuch that localid="1649404108890" 35%of all observations from a standard Normal distribution are greater than localid="1649404115271" z.

- Use Table A to find the percentile of a value from any Normal distribution and the value that corresponds to a given percentile.

Carbon dioxide emissions The figure below is a Normal probability plot of the emissions of carbon dioxide per person in 48countries.15In what ways is this distribution non-Normal?

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?
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