Question

Suppose that 75% of all dialysis patients will survive for at least 5 years.

In a simple random sample of 100 new dialysis patients, what is the probability that the proportion surviving for at least five years will exceed 80%, rounded to 5 decimal places?

Answer 1

for normal distribution z score =(p̂-p)/σp
here population proportion=     p=	0.750
sample size       =n=	100
std error of proportion=σp=√(p*(1-p)/n)=	0.0433

probability =

P(X>0.8)

=

P(Z>1.15)=

1-P(Z<1.15)=

1-0.87589=

0.12411