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?

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