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Chapter 8: Q. 8.13 (page 391)

Student scores on exams given by a certain instructor have mean 74 and standard deviation 14. This instructor is about to give two exams, one to a class of size 25 and the other to a class of size 64.

(a) Approximate the probability that the average test score in the class of size 25 exceeds 80.

(b) Repeat part (a) for the class of size 64.

(c) Approximate the probability that the average test score in the larger class exceeds that of the other class by more than 2.2 points.

(d) Approximate the probability that the average test score in the smaller class exceeds that of the other class.

by more than 2.2 points.

Short Answer

Expert verified

The summary of the solution is as follows

a.)P(X>80)鈮�0.0162b.)P(Y>80)鈮�0.0003c.)P(Y-X>2.2)鈮�0.2514d.)P(Y-X<2.2)鈮�0.7485

Step by step solution

01

Given Information

饾渿=74,饾湈=14,n=25andm=64

where symbols have their usual meanings.

02

Part (a)

P(X>80)=PX-7414/5>157鈮�P(Z>2.14)鈮�0.0162

03

Part (b)

P(Y>80)=PY-7414/8>247鈮�P(Z>3.43)鈮�0.0003

04

Part (c)

We have

SD(Y-X)=196/64+196/25鈮�3.33

Therefore

P(Y-X>2.2)=PY-X3.3>2.23.3鈮�P(Z>0.6667)鈮�0.2514

05

Part (d)

Using part (c) we get

P(Y-X<2.2)鈮�0.7485

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Most popular questions from this chapter

8.5 The amount of time that a certain type of component functions before failing is a random variable with probability density function

f(x)=2x0<x<1

Once the component fails, it is immediately replaced by
another one of the same type. If we let denote the life-time of the ith component to be put in use, then Sn=鈭�i=1nXirepresents the time of the nth failure. The long-term rate at which failures occur, call itr, is defined by
r=limn鈫�鈭�nSn

Assuming that the random variables Xi,i鈮�1,are independent, determine r.

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Explain why a gamma random variable with parameters(t,位)has an approximately normal distribution whentis large.

Each new book donated to a library must be processed. Suppose that the time it takes to process a book has a mean of 10minutes and a standard deviation of 3minutes. If a librarian has 40 books to process,

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