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Chapter 4: Q. AP1.3 (page 293)

A large set of test scores has mean 60and standard deviation 18. If each score is doubled, and then 5is subtracted from the result, the mean and standard deviation of the new scores are

a. mean 115and standard deviation 31.

b. mean 115and standard deviation 36.

c. mean 120and standard deviation 6.

d. mean 120and standard deviation 31.

e. mean 120and standard deviation 36.

Short Answer

Expert verified

The standard deviation of the new scores are (b) mean115and standard deviation36.

Step by step solution

01

Given Information

We have been given that the mean (渭) = 60and standard deviation (蟽) =18. All scores are then doubled and decreased by 5.

02

Simplification

Since the mean is a measure of a center, it is influenced in the same way that the scores are, so the mean is doubled and reduced by 5.

渭new=2渭-5

渭new=2脳60-5

渭new=115.

Since the standard deviation is also the measure of spread, the standard deviation is also doubled but not decreased by 5.

localid="1653802755720" 蟽new=2蟽=2脳18=36

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