Question

A random sample of size n = 100 is taken from a population of size N = 600 with a population proportion of p =0.46. Is it necessary to apply the finite population correction factor? Calculate the expected value and standard error of the sample proportion. What is the probability that the sample mean is less than .40?

Answer 1

Solution :

There is not necessary to apply the finite population correction factor .

Given that,

Expected value ,

= p = 0.46

Standard error is,

=  [p( 1 - p ) / n = [(0.46 * 0.54) / 100] = 0.04984

P( < 0.40) =

= P[( - ) / < (0.40 - 0.46) / 0.04984]

= P(z < -1.20)

= 0.1151

Probability = 0.1151