A company with several branches all across the country and t

A company, with several branches all across the country and thousands of employees, claims that 46% of their employees are female. To test this claim an independant statistical company took a sample of 50 employees and recorded the proportion found to be female.

a) Assuming the claim is true, what is the probability that the percentage of females in the sample is less than 43%?

Solution

Normal Distribution
Proportion ( P ) =0.46
Standard Deviation ( sd )= Sqrt (P*Q /n) = Sqrt(0.46*0.54/50)
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P(X < 0.43) = (0.43-0.46)/0.0705
= -0.03/0.0705= -0.4255
= P ( Z <-0.4255) From Standard Normal Table
= 0.3352