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Chapter 6: Q. 49 (page 389)

El Dorado Community College has a main campus in the suburbs and a downtown campus. The amount X spent on tuition by a randomly selected student at the main campus has mean 732.50 and standard deviation 103. The amount Y spent on tuition by a randomly selected student at the downtown campus has mean 825 and standard deviation 126.50. Suppose we randomly select one full-time student from each of the two campuses. Calculate and interpret the mean of the sumS=X+Y.

Short Answer

Expert verified

The Average mean of the main campus and downtown campus is15570.50

Step by step solution

01

Given information

The main campus mean 732.50, standard deviation 103

The downtown campus mean 825,standard deviation 126.50

μX=732.50σX=103μY=825σY=126.50

X = Amount spent on tuition by students on the main campus who were chosen at random.

Y= Amount spent on tuition by students on the downtown campus who were chosen at random.

02

Calculations

μ=μX+μY=732.50+825=1557.50

There are two mean of two unique irregular factors μX=732.50 and μY=825 so the mean of the two arbitrary variable will be the amount of their means. The aggregate sum spent on both the principal grounds and downtown grounds will be normal15570.50

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Most popular questions from this chapter

Exercises 21 and 22 examine how Benford’s law (Exercise 9) can be used to detect fraud.

Benford’s law and fraud A not-so-clever employee decided to fake his monthly expense report. He believed that the first digits of his expense amounts should be equally likely to be any of the numbers from 1 to 9. In that case, the first digit Yof a randomly selected expense amount would have the probability distribution shown in the histogram.

(a) What’s P(Y<6)? According to Benford’s law (see Exercise 9), what proportion of first digits in the employee’s expense amounts should be greater than 6? How could this information be used to detect a fake expense report?

(b) Explain why the mean of the random variable Yis located at the solid red line in the figure.

(c) According to Benford’s law, the expected value of the first digit is μX=3.441. Explain how this information could be used to detect a fake expense report.

Running a mile A study of 12,000able-bodied male students at the University of Illinois found that their times for the mile run were approximately Normal with mean 7.11 minutes and standard deviation 0.74 minute. 7 Choose a student at random from this group and call his time for the mile Y. Find P(Y<6). Interpret this value.

Let Y denote the number of broken eggs in a randomly selected carton of one dozen “store brand” eggs at a local supermarket. Suppose that the probability distribution of Y is as follows.

Valueyi01234
ProbabilityPi0.78
0.11
0.07
0.03
0.01

a. What is the probability that at least 10 eggs in a randomly selected carton are unbroken?

b. Calculate and interpret μY.

C. Calculate and interpret σY.

d. A quality control inspector at the store keeps looking at randomly selected cartons of eggs until he finds one with at least 2 broken eggs. Find the probability that this happens in one of the first three cartons he inspects.

Ed and Adelaide attend the same high school but are in different math classes. The time E that it takes Ed to do his math homework follows a Normal distribution with mean 25 minutes and standard deviation 5 minutes. Adelaide's math homework time A follows a Normal distribution with mean 50 minutes and standard deviation 10 minutes. Assume that E and A are independent random variables.

a. Randomly select one math assignment of Ed's and one math assignment of Adelaide's. Let the random variable D be the difference in the amount of time each student spent on their assignments: D=A-E. Find the mean and the standard deviation of D.

b. Find the probability that Ed spent longer on his assignment than Adelaide did on hers.

In debt? Refer to Exercise 100.

a. Justify why D can be approximated by a normal distribution.

b. Use a normal distribution to estimate the probability that 30or more adults in the sample have more debt than savings.
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