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The literacy rate for a nation measures the proportion of people age 15 and over who can read and write. The literacy rate for women in Afghanistan is 12%. Let X = the number of Afghani women you ask until one says that she is literate.

a. What is the probability distribution of X?

b. What is the probability that you ask five women before one says she is literate?

c. What is the probability that you must ask ten women?

d. Find the (i) mean and (ii) standard deviation of X.

Short Answer

Expert verified

a. X follows geometric distribution with the parameters X~G(0.12)

b. The probability that you ask five women before one says she is literate 0.4723

c. The probability that you must ask ten women 0.7125

d.mean=8.333standarddeviation=7.82

Step by step solution

01

Content Introduction

We are given,

The literacy rate for women in Afghanistan is 12%

X = the number of Afghani women

02

Explanation (Part a)

Let X the number of women ask until one says she is literature. The sample size X takes on the values 0,1,2,3,......with probability p=0.12

Therefore, X follows geometric distribution with the parameters,X~G(0.12)

03

Explanation (Part b)

Let X the number of women ask until one says she is literature. The sample size X takes on the values 0,1,2,3,......with probability p=0.12

Therefore, X follows geometric distribution with the parameters, X~G(0.12)

To find the probability that X=5step in T1-83+ calculator is as follow:

Press 1and then press 2ndDISTR

Arrow down to geometpdf. Press ENTER

Enter (0.12,5)

The result showsP(X=5)=0.4723

04

Explanation (Part c)

Let X the number of women ask until one says she is literature. The sample size X takes on the values 0,1,2,3,......with probability p=0.12

Therefore, X follows geometric distribution with the parameters X~G(0.12)

To find the probability that X=10step in T1-83+ calculator is as follow:

Press 1and then press 2ndDISTR

Arrow down to geometpdf. Press ENTER

Enter (0.12,10)

The result showsP(X=10)=0.7215

05

Explanation (Part d)

Let X the number of women ask until one says she is literature. The sample size X takes on the values 0,1,2,3,......with probability p=0.12

Therefore, X follows geometric distribution with the parameters X~G(0.12)

Mean()=1pstandarddeviation()=1-pp2

Substitute the value

mean()=10.12mean()=8.333Standarddeviation()=1-0.12(0.12)2Standarddeviation()=7.82

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