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Ms. Hall gave her class a 10-question multiple-choice quiz. Let X=the number of questions that a randomly selected student in the class answered correctly. The computer output below gives information about the probability distribution of X. To determine each student鈥檚 grade on the quiz (out of localid="1649489099543" 100), Ms. Hall will multiply his or her number of correct answers by 10. Let localid="1649489106434" G=the grade of a randomly chosen student in the class.

localid="1649489113566" NMeanMedianStDevMinMaxQ1Q3307.68.51.3241089

(a) Find the mean of localid="1649489121120" G. Show your method.

(b) Find the standard deviation of localid="1649489127059" G. Show your method.

(c) How do the variance of localid="1649489132289" Xand the variance oflocalid="1649489138146" Gcompare? Justify your answer.

Short Answer

Expert verified

(a) The mean of Gis localid="1649489147240" G=76.

(b) The standard deviation of Gis G=13.2.

(c) The variance of Gis 100times the variance of X.

G2=100X2

Step by step solution

01

Part (a) Step 1: Given Information 

In the output, the mean for the variable Xis given:

X=7.6

02

Part (a) Step 2: Explanation

Ms. Hall multiplies the number of correct answers Xby 10:

G=10X

Property mean:

aX+b=aX+b

Then we can determine the mean for G:

localid="1649909794929" G=10X=10X=10(7.6)=76

03

Part (b) Step 1: Given Information 

In the output, the standard deviation "StDev" for the variable Xis given:

X=1.32

04

Part (b) Step 2: Explanation 

Ms. Hall multiplies the number of correct answers Xby 10:

G=10X

Property standard deviation:

aX+b=aX

Then we can determine the standard deviation for G:

localid="1649909831105" G=10X=10X=10(1.32)=13.2

05

Part (c) Step 1: Given Information 

Given

NMeanMedianStDevMinMaxQ1Q3307.68.51.3241089

06

Part (c) Step 2: Explanation 

Ms. Hall multiplies the number of correct answers Xby 10:

G=10X

Property standard deviation:

aX+b=aX

Then we can determine the standard deviation for G:

localid="1649909863743" G=10X=10X

The variance is the square of the standard deviation:

localid="1649909871172" G2=102X2=100X2

Thus the variance of Gis 100times the variance of X.

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