Log out Go to App
Go to App

Learning Materials

Features

Discover

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

Step by step solution

01

Given Information

𝜇=74,𝜎=14,n=25andm=64

where symbols have their usual meanings.

02

Part (a)

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

03

Part (b)

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

04

Part (c)

We have

SD(Y-X)=196/64+196/25≈3.33

Therefore

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

05

Part (d)

Using part (c) we get

P(Y-X<2.2)≈0.7485

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Each of the batteries in a collection of 40batteries is equally likely to be either a type A or a type B battery. Type A batteries last for an amount of time that has a mean of 50and a standard deviation of 15; type B batteries last for a mean of 30and a standard deviation of 6.

(a) Approximate the probability that the total life of all 40batteries exceeds 1700

(b) Suppose it is known that 20of the batteries are type A and 20are type B. Now approximate the probability that the total life of all 40batteries exceeds 1700.

It Xhas a varianceσ2, then σ, the positive square root of the variance, is called the standard deviation. It Xhas to mean μand standard deviationσ, to show thatP{|X-μ|≥kσ}≤1k2.

From past experience, a professor knows that the test score taking her final examination is a random variable with a mean of75.

(a)Give an upper bound for the probability that a student’s test score will exceed85.

(b)Suppose, in addition, that the professor knows that the variance of a student’s test score is equal25. What can be said about the probability that a student will score between 65and85?

(c)How many students would have to take the examination to ensure a probability of at least .9that the class average would be within 5of75? Do not use the central limit theorem.

Suppose a fair coin is tossed 1000times. If the first 100tosses all result in heads, what proportion of heads would you expect on the final900tosses? Comment on the statement “The strong law of large numbers swamps but does not compensate.”

Suppose that X is a random variable with mean and variance both equal to 20. What can be said about P{0 < X < 40}?
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free