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Chapter 6: Q. 2.1 (page 390)

To introduce her class to binomial distributions, Mrs. Desai gives a 10 -item, multiple-choice quiz. The catch is, that students must simply guess an answer (A through E) for each question. Mrs. Desai uses her computer's random number generator to produce the answer key so that each possible answer has an equal chance to be chosen. Patti is one of the students in this class. Let X=the number of Patti's correct guesses.

1. Show that Xis a binomial random variable.

Short Answer

Expert verified

It has been shown thatXis a binomial random variable.

Step by step solution

01

Given Information 

Mr. Desai gives =10times

X=The number of Patti's correct guesses.

02

Explanation

The algorithm chose correct responses at random, thus one trial should not alter the outcome of the others.

There were ten questions in total.

Each trial has a0.20 chance of succeeding.

As a result, this is a binomial situation.

Because it counts the number of successes, Xis a binomial random variable withn=10and p=0.20.

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Most popular questions from this chapter

A large auto dealership keeps track of sales and leases agreements made during each hour of the day. Let X= the number of cars sold and Y= the number of cars leased during the 铿乺st hour of business on a randomly selected Friday. Based on previous records, the probability distributions of Xand Yare as follows:

顿别铿乶别 T=X+Y.

Find and interpret 渭T.

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(b) When an opinion poll calls residential telephone numbers at random, only 20%of the calls reach a live person. You watch the random digit dialing machine make calls. Yis the number of calls until the first live person answers

As the dangers of smoking have become more widely known, clear class differences in smoking have emerged. British government statistics classify adult men by occupation as 鈥渕anagerial and professional鈥� (43%of the population), 鈥渋ntermediate鈥� (34%), or 鈥渞outine and manual鈥� (23%). A survey finds that 20%of men in managerial and professional occupations smoke, 29%of the intermediate group smoke, and 38%in routine and manual occupations smoke.

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50. Checking independence For each of the following situations, would you expect the random variables Xand Yto be independent? Explain your answers.

(a)Xis the rainfall (in inches) on November 6of this year, and Yis the rainfall at the same location on November 6 of next year.
(b) Xis the amount of rainfall today, and Y is the rainfall at the same location tomorrow.
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Refer to the previous Check Your Understanding (page 390 ) about Mrs. Desai's special multiple-choice quiz on binomial distributions. We defined X=the number of Patti's correct guesses.

1. Find 渭X. Interpret this value in context.

2. Find localid="1649452775386" 蟽X. Interpret this value in context.
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