A random sample is to be selected from a population that has

A random sample is to be selected from a population that has a proportion of successes p= 0.75. a. Determine the mean and standard deviation of the sample proportion p when the sample size n=400

. b. For n=400, what is P (0.7 < p < 0.8)

Solution

Mean = p

Here, p=0.75 , q=0.25 , n=400

a) Mean = p = 0.75

Standard deviation = 0.0216.

b) P (0.7 < p < 0.8) = P( -2.31 < z < 2.31 ) = 0.4896*2 = 0.9792.