Question

Suppose the CPA Practice Advisor reports that the mean preparation fee for 2017 federal income tax returns was $273. Use this price as the population mean and assume the population standard deviation of preparation fees is $100.

(a)What is the probability that the mean price for a sample of 20 federal income tax returns is within $16 of the population mean? (Round your answer to four decimal places.)

(b)What is the probability that the mean price for a sample of 60 federal income tax returns is within $16 of the population mean? (Round your answer to four decimal places.)

(c)What is the probability that the mean price for a sample of 121 federal income tax returns is within $16 of the population mean?(Round your answer to four decimal places.)

(d)Which, if any, of the sample sizes in parts (a), (b), and (c) would you recommend to ensure at least a 0.95 probability that the sample mean is within $16 of the population mean? (Select all that apply.)

20 customers

60 customers

121 customers

none of the above

Answer 1

a)

for normal distribution z score =(X-μ)/σx
here mean=       μ=	273
std deviation   =σ=	100.000
sample size       =n=	20
std error=σx̅=σ/√n=	22.3607

probability =

P(257<X<289)

=

P(-0.72<Z<0.72)=

0.7642-0.2358=

0.5284

b)

std error=σx̅=σ/√n=

12.9099

probability =

P(257<X<289)

=

P(-1.24<Z<1.24)=

0.8925-0.1075=

0.7850

c)

std error=σx̅=σ/√n=

9.0909

probability =

P(257<X<289)

=

P(-1.76<Z<1.76)=

0.9608-0.0392=

0.9216

d)

none of the above :as probability is less than 0.95 in each of above 3 cases