when an opinion poll calls landline telephone numbers at random, approximately 35% of the numbers are working residential phone numbers. The remainder are either non-residential, non-working, or computer/fax numbers. You watch the random dialing machine make 20 calls. (a) What is the mean number of calls that reach working residential numbers? (Enter your answer to one decimal place.) calls (b) What is the standard deviation ? of the count of calls that reach working residential numbers? (Round your answer to four decimal places.) calls (c) Suppose that the probability of reaching a working residential number was only p = 0.25. How does this new p affect the standard deviation? (Round your answer to four decimal places.) calls (d) What would be the standard deviation if p = 0.10? (Round your answer to four decimal places.) calls (e) What does your work show about the behavior of the standard deviation of a binomial distribution as the probability of a success gets closer to zero? As p approaches 0, the standard deviation increases. As p approaches 0, the standard deviation rises then falls. As p approaches 0, the standard deviation falls then rises. As p approaches 0, the standard deviation decreases. As p approaches 0, the standard deviation remains constant.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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Question

when an opinion poll calls landline telephone numbers at random, approximately 35% of the numbers are working residential phone numbers. The remainder are either non-residential, non-working, or computer/fax numbers. You watch the random dialing machine make 20 calls.

(a) What is the mean number of calls that reach working residential numbers? (Enter your answer to one decimal place.)
calls

(b) What is the standard deviation ? of the count of calls that reach working residential numbers? (Round your answer to four decimal places.)
calls

(c) Suppose that the probability of reaching a working residential number was only

p = 0.25.

How does this new p affect the standard deviation? (Round your answer to four decimal places.)
calls

(d) What would be the standard deviation if

p = 0.10?

(Round your answer to four decimal places.)
calls

(e) What does your work show about the behavior of the standard deviation of a binomial distribution as the probability of a success gets closer to zero?

As p approaches 0, the standard deviation increases.

As p approaches 0, the standard deviation rises then falls.

As p approaches 0, the standard deviation falls then rises.

As p approaches 0, the standard deviation decreases.

As p approaches 0, the standard deviation remains constant.

Expert Solution

Step 1

Binomial distribution: A discrete r.v. X taking values 0,1,2,3, …., n is said to follow a binomial distribution with parameters n and p if it's p.m.f is given by,

Given,

Sample size = n = 20

Probability of success = p = 35% = 0.35

q = 1-p = 1-0.35 = 0.65

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