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Chapter 2: Q 26. (page 107)

Step right up! Refer to Exercise 22 Suppose that the distances from the tops of the students鈥� heads to the ground are converted from inches to feet (note that 12in.=1ft).

a. What shape would the resulting distribution have? Explain your answer.

b. Find the mean of the distribution of distance in feet.

c. Find the standard deviation of the distribution of distance in feet.

Short Answer

Expert verified

Part (a) The distribution is skewed to right with a single peak.

Part (b) Mean of the distribution of distance is 6.083feet.

Part (c) Standard deviation of the distribution of the distance is 0.3575 feet.

Step by step solution

01

Part (a) Step 1: Given information

12in.=1ft

Every distance value in inches must be reduced by 12 to convert from inches to feet.

02

Part (a) Step 2: Explanation

We discovered that the distribution of distances was skewed to the right, with a single peak. When every value in the data is split by 12the form of the distribution remains unchanged since the associations between each data pair remain unchanged. As a result, the form of the distance distribution, in this case, is also skewed to the right, with a single peak.

03

Part (b) Step 1: Calculation

We discovered that the mean of the distance distribution was 73inches. We must divide the mean in inches by 12to translate the mean of the distribution of distances from inches to feet.

x=7312=6.083ft.

Thus,

The mean of the distribution of distance in feet is 6.083 feet.

04

Part (c) Step 1: Calculation

Standard deviation, sx=4.29in.

We discovered that the standard deviation of the distance distribution was 4.29inches. We must divide the standard deviation in inches by 12to convert the standard deviation of a distribution of lengths from inches to feet.

sx=4.2912=0.3575ft.

Thus,

The standard deviation of the distribution of distance in feet is 0.3575 feet.

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