About 77 of all female heart transplant patients will surviv

About 77% of all female heart transplant patients will survive for at least 3 years. One hundred five female heart transplant patients are randomly selected. What is the probability that the sample proportion surviving for at least 3 years will be less than 70%?

Steps please! :)

Solution

About 77% of all female heart transplant patients will survive for at least 3 years. One hundred five female heart transplant patients are randomly selected. What is the probability that the sample proportion surviving for at least 3 years will be less than 70%?

Steps please! :)

n=105

p=0.77

np and n(1-p) both > 10, normal approximation used

standard error of p = sqrt( p(1-p)/n)) = sqrt( 0.77*0.23/105) = 0.0411

z value for p=0.70 is   z = ( 0.70-0.77)/0.0411 = -1.70

P( p < 0.70) = P( z < -1.7) = 0.0446