A department store has determined that 25% of all their sales are credit sales. A random sample of 75 sales is selected and the proportion of credit sales in the sample is computed.

Question

a) What is the probability that the same proportion will be greater than 0.34?

In a random sample of N, the most likely number of credit sales will be
m = 0.25 N,
and the standard deviation of the distribution is
sigma = sqrt (N*0.25*0.75) = 0.433sqrt N
When N= 75, m = 18.75 sigma = 3.75
If the number of credit sales is 0.34N, that is 25.5.
Using the normal distribution tool of
http://psych.colorado.edu/~mcclella/java/normal/accurateNormal.html ,
I get the probability to be 3.6%

just to make sure i did this right.

What is the probability that the sample proportion will be between 0.196 and 0.354?

The answer i got is 84.12%

And the probability that the sample proportion will be less than 0.25 is 50%?

I have one question, from looking at the textbook, it says that the mean and standard deviation of a sample proportion is mu=p and sigma=sqrt(p(1-p)/n)

why would you not use this equation instead?

nevermind, it actually gave the same answer.