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Chapter 4: Q. 103 (page 295)

The literacy rate for a nation measures the proportion of people age 15 and over that can read and write. The literacy rate in Afghanistan is 28.1%. Suppose you choose 15 people in Afghanistan at random. Let X = the number of people who are literate.

a. Sketch a graph of the probability distribution of X.

b. Using the formulas, calculate the (i) mean and (ii) standard deviation of X.

c. Find the probability that more than five people in the sample are literate. Is it is more likely that three people or four people are literate.

Short Answer

Expert verified

a.

b. mean is 4.215and standard deviation is 1.749

c. The probability of three people or four people are literate is P(X=3or4)=0.4185and the probability that more than five people in the sample are literate is P(X>5)=0.2246

Step by step solution

01

Content Introduction

The binomial distribution determines the probability of looking at a specific quantity of a hit results in a specific quantity of trials.

02

Explanation (part a)

The graphic presentation of X is:

03

Explanation (part b)

Let us first check the distribution of X:

we are given n=15,p=0.281

the distribution of X is (15,0.281)

The mean is

渭=np渭=15脳0.281渭=4.215

The standard deviation is:

蟽=np(1-p)蟽=15脳0.281(1-0.281)蟽=1.749

04

Explanation (part c)

The probability for three people or four people are literate is:

P(X=3or4)=153(0.281)3(0.719)12+154(0.281)4(0.719)11P(X=3or4)=0.1926+0.2259P(X=3or4)=0.4185

The probability that more than five people in the sample are literate is:

P(X>5)=1-P(X=0)-P(X=1)-P(X=2)-P(X=3)-P(X=4)P(X>5)=0.2246

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