what proportion of samples would be composed of samples with p-hat between .44 and .54

Question

Assume that you will be taking samples from a population with a proportion P = 44%. With n = 100, what proportion of the resulting sampling distribution will be between .44 and .54? Asked another way, what proportion of samples would be composed of samples with p-hat between .44 and .54

Show all work and calculation please!

Answer 1

want to find P(0.44 < phat < 0.54)

transform end points of above inequality using

z = (phat - P)/sqrt(P*(1-P)/n)

compute z-lower for phat = 0.44

compute z-upper for phat = 0.54

so probability interval becomes (z-lower < phat < z-upper)

user normal probability tables to compute probability