Question

About 73​% of all female heart transplant patients will survive for at least 3 years. Seventy 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 66​%? 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 to StartRoot StartFraction pq Over n EndFraction EndRoot .

The probability that the sample proportion surviving for at least 3 years will be less than 66​% is

Answer 1

Solution

Given that,

p = 0.73

1 - p = 1 - 0.73 = 0.27

n = 70

= p = 0.73

=  [p ( 1 - p ) / n] =   [(0.73 * 0.27) / 70 ] = 0.0531

P( < 0.66)

= P[( - ) / < (0.66 - 0.73) / 0.0531]

= P(z < -1.32)

Using z table,

= 0.0934