Question

The mean preparation fee H&R Block charged for taxes in 2012 was $183. Use this price as a population mean and assume the SD of the population is $50.

a) What is the probability that the mean price for a sample of 30 H&R Block customer is within $8 of the population mean?

b) What is the probability that the mean price for a sample of 50 H&R Block customer is within $8 of the population mean?

c). What is the probability that the mean price for a sample of 100 H&R Block customer is within $8 of the population mean?

d) Which, if any, of the sample sizes in parts (a),(b),(c) would you recommend to have at least 95% probability that the sample mean is within $8 of the population mean?

Answer 1

a)

standard deviation σ=	50
sample size       =n=	30
std error=σx̅=σ/√n=	9.1287

probability =P((-8-0)/9.129)<Z<(8-0)/9.129)=P(-0.88<Z<0.88)=0.8106-0.1894=0.6212

b)

sample size       =n=	50
std error=σx̅=σ/√n=	7.0711

probability =P((-8-0)/7.071)<Z<(8-0)/7.071)=P(-1.13<Z<1.13)=0.8708-0.1292=0.7416

c)

sample size       =n=	100
std error=σx̅=σ/√n=	5.0000

probability =P((-8-0)/5)<Z<(8-0)/5)=P(-1.6<Z<1.6)=0.9452-0.0548=0.8904

d)

here since none of the samples give probability at least 95%, none of the above samples give at least 95% probability that the sample mean is within $8 of the population mean