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Chapter 12: Q. 34 (page 805)

A distribution of exam scores has mean 60and standard deviation 18. If each score is doubled, and then 5is subtracted from that result, what will be the mean and standard deviation, respectively, of the new scores?

(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=120 and standard deviation=36

Short Answer

Expert verified

The answer is mean115and standard deviation 36. so option (b) is correct.

Step by step solution

01

Given Information

We are given that the mean is μx=60and standard deviation is σx=18and we have to find out mean and standard deviation when 5is subtracted from the result.

02

Explanation

Now as we have old mean and standard deviation,

which gives 60 and 18 respectively,

But there is a property of mean and standard deviation,

μax+b=aμx+b(property of mean)

σax+b=aσx(property of standard deviation)

Now ax+b=2x-5

and putting this in the properties,

we get,μ2x-5=2μx-5=2(60)-5

On solving we get newmean=115

and also, σ2x-5=2σx=2(18)

On solving we get, newstandarddeviation=36

Hence, option (b) is correct.

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