Question

7) To estimate the mean acreage of ranches in a certain province a resear cher plans to obtain the acreage for arand om sample of 64 farms Results from an earlier study suggest that 800 acr es is a reasonable guess for the standard deviation of ranch size. 7) a. Find the probability that the samplemean acr eage falls within 100 acres of the population mean acreage. b. If the researcher can increase n above 64, will the probability that the sample mean falls within 100 acr es of the popu lation mean increase or decrease? Why?

Answer 1

Ans:

a)

sample size,n=64

standard deviation=800

standard error of mean=800/sqrt(64)=100

z=+/-100/100=+/-1

P(-1<z<1)=P(z<1)-P(z<-1)

=0.8413-0.1587=0.6826

b)If n increases,the probability that sample mean falls within 100 acres of the population mean will increase,as standard error will decrease.