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Chapter 6: Q. 66 (page 382)

The standard deviation of Tis

(a)22

(b) 16

(c)15.62

(d)11.66

(e)4

Short Answer

Expert verified

The standard deviation of Tis option(d)11.66

Step by step solution

01

Concept Introduction

The standard deviation of a set of data describes how far values deviate from the mean, with a greater standard deviation indicating a wider range of variance. A low standard deviation implies that the values are close to the mean, whereas a high standard deviation shows that the data are dispersed over a wider range.

02

Explanation 

Given

μX=110

σX=10

μY=140

σY=12

Property mean and variance (if Xand Yare independent):

localid="1649858464290" μaX+bY=aμX+bμYσaX+bY2=a2μX2+b2μY2

Results we obtain:

localid="1649858468484" μX+Y/2=μX+12μY=110+12(140)=180σX+Y/2=σX2+122σX22=102+14122≈11.66.

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