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Chapter 6: Q. 57 (page 392)

Community college costs : Refer to Exercise 49.

Note that XandY are independent random variables because the two students are randomly selected from each of the campuses. Calculate and interpret the standard deviation of the sum S=X+Y.

Short Answer

Expert verified

The total amount spent on both the Downtown and Main campuses differs by $163.3 on average from the mean amount spent of$1,557.50.

Step by step solution

01

Given Information

Given :

X: The amount spent on tuition by a randomly selected student at Main campus

Y: The amount spent on tuition by a randomly selected student at Downtown campus

02

Calculating and interpreting the standard deviation of the sumS = X + Y.

Total mean of the mean amount spent by both X and Y is given by :

μX+Y=732.50+825=$1,557.50

The variance of the total is equal to the sum of the variances of the random variables when they are independent.

role="math" localid="1654176112869" σ2X+Y=σ2X+σ2Y=(103)2+(126.50)2=$26611.25

We also know that the standard deviation equals the variance squared:

σX+Y=σ2X+Y=26611.25=$163.13

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