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.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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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