The Institute of College Access and Success report that 67 o

The Institute of College Access and Success report that 67% of college students in 2008 graduates with student loan debt a random sample of 85 graduates is drawn.

A. Find the mean U- P- Hat.
B. Find the standard deviation of p-hat.
C. Find the probability that between 65% and 80% of the people in the sample were in debt.

Solution

The Institute of College Access and Success report that 67% of college students in 2008 graduates with student loan debt a random sample of 85 graduates is drawn.

A. Find the mean U- P- Hat.
p=0.67

B. Find the standard deviation of p-hat.

Sd= sqrt( p*(1-p)/n) = sqrt(0.67( 1-0.67)/85) = 0.051

C. Find the probability that between 65% and 80% of the people in the sample were in debt.

Z value or 65%, z=( 0.65-0.67)/0.051 =-0.39

Z value or 80%, z=( 0.80-0.67)/0.051 =2.55

P(-0.39<z<2.55)

= P( z<2.55) – P( z < -0.39)

= 0.9946 - 0.3483

=0.6463

probability that between 65% and 80% of the people in the sample were in debt =0.6463