Question

The Wall Street Journal reports that 33% of taxpayers with adjusted gross incomes between $30,000 and $60,000 itemized deductions on their federal income tax return. The mean amount of deductions for this population of taxpayers was $16,642. Assume the standard deviation is

σ = $2,400.

(a)

What is the probability that a sample of taxpayers from this income group who have itemized deductions will show a sample mean within $200 of the population mean for each of the following sample sizes:150, and 300? (Round your answers to four decimal places.)

sample size n = 150

sample size n = 300

Answer 1

Solution :

sample size n = 150

= / n = 2400 / 150 = 195.9592

= P[ -200 / 195.9592 < ( - ) / < 200 / 195.9592)]

= P(-1.02 < Z < 1.02)

= P(Z < 1.02) - P(Z < -1.02)

=  0.6923

sample size n = 300

= 2400 / 300 = 138.5641

= P[ -200 / 138.5641 < ( - ) / < 200 / 138.5641)]

= P(-1.44 < Z < 1.44)

= P(Z < 1.44) - P(Z < -1.44)

= 0.8501