Question

About 72​% of all female heart transplant patients will survive for at least 3 years. Ninety 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 65%? Assume the sampling distribution of sample proportions is a normal distribution. The mean of the sample proportion is equal to the population proportion and the standard deviation is equal root pq/ n.

The probability that the sample proportion surviving for at least 3 years will be less than 65% is nothing. ​(Round to four decimal places as​ needed.)

Answer 1

n = 90

p = 0.72

= p = 0.72

= sqrt(p(1 - p)/n)

       = sqrt(0.72 * (1 - 0.72)/90)

       = 0.0473

P( < 0.65)

= P(( - )/ < (0.65 - )/)

= P(Z < (0.65 - 0.72)/0.0473)

= P(Z < -1.48)

= 0.0694