A university administrator expects that 25 of students in a

A university administrator expects that 25% of students in a core course will receive an A. He looks at the grades assigned to 60 students.

The probability that the proportion of students who receive an A is between 0.20 and 0.35 is _________.

Solution

So the probability is

P(0.2<phat<0.35)

=P((0.2-0.25)/sqrt(0.25*0.75/60) <(phat-p)/sqrt(p*(1-p)/n) <(0.35-0.25)/sqrt(0.25*0.75/60))

=P(-0.89<Z<1.79)

=0.7766 (from standard normal table)

Answer: 0.7766