Question

os nq the establshment of a new bank in a community an existinq ban stated that the area to b served b th?pronated bank conta ned 70 pa cent at its accounts. An orono me consut nq mmm random sar led th ho sahalds to dat ermine the sample pranar on hich had accounts existing bank. The sample size was 225. (Round your answers)t 3 detimal places. Find the probability that , is a. Less than G percent. b. Monethan 78 percent.

Answer 1

Ans:

Sampling distribution of sample proportions:

Given that

population proportion,p=0.7

n=225

mean=0.7

standard deviation=sqrt(0.7*(1-0.7)/225)=0.0306

a)sample proportion=0.6

z=(0.6-0.7)/0.0306=-3.27

P(z<-3.27)=0.001

b)sample proportion=0.78

z=(0.78-0.7)/0.0306=2.62

P(z>2.62)=0.004