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Among the adults in a large city, 30% have a college

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 10E Chapter 4.11

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 10E

Problem 10E

Among the adults in a large city, 30% have a college degree. A simple random sample of 100 adults is chosen. What is the probability that more than 35 of them have a college degree?

Step-by-Step Solution:

Solution

Step 1 of 2

Here we need to find the probability of more than 35 of them having college degree

Given that 30% having the college degree p=0.30

A random sample of 100 is chosen n=100

Let X represents no. of adults having college degree

XB(100,0.3)

So X is approximately following the normal distribution with

Mean=np

        =100(0.3)

        =30

Variance =npq

               =100(0.3)(0.7)

               =21

Hence =

              =4.6


Step 1 of 2

Now we have to find P(X>35)

Here Z=(

           =(35-30)/4.6

           =1.09

Now find P(Z>1.09) value from the standard normal tables

P(Z>1.09)=1-P(Z1.09)

                =1-0.86214

                =0.13786

Hence the probability of more than 35 of them having college degree is 0.13786


Step 2 of 1

Chapter 4.11, Problem 10E is Solved
Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

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Among the adults in a large city, 30% have a college