A study of mininum wage earners found that 22 of them are 16

A study of mininum wage earners found that 22% of them are 16-24 years old. Suppose that a random sample of 500 minimum wage earnersis selected. What is the probabilty that at most 120 of them are 16-24 years old? Use the normal curve approximation to the binomial distribution.

The probability is ____?        

Round to four decimal places as needed.

Solution

Normal Approximation to Binomial Distribution
Mean ( np ) =500 * 0.22 = 110
Standard Deviation ( npq )= 500*0.22*0.78 = 9.2628
Normal Distribution = Z= X- u / sd                   
P(X > 120) = (120-110)/9.2628
= 10/9.2628 = 1.0796
= P ( Z >1.08) From Standard Normal Table
= 0.1402                  
P( probabilty that at most 120 of them are 16-24 years old) = 1 - P(X > 120)
= 1 - 0.1402
= 0.8598