Question

For the year 2010, 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: 20, 60, 150, and 400? (Round your answers to four decimal places.)

sample size n = 20 =________

Answer 1

$200 within population mean means 200 below and 200 above the population mean

so, lower = 16642 - 200 = 16442

upper = 16642 + 200 = 16842

(A) when n = 20

using normalcdf

setting lower = 16442, upper = 16842, mean = 16642 and sigma = 2400/sqrt(20)

=normalcdf(16842,16442,16642,2400/sqrt(20))

= 0.2906

(B) when n = 60

using normalcdf

setting lower = 16442, upper = 16842, mean = 16642 and sigma = 2400/sqrt(60)

=normalcdf(16842,16442,16642,2400/sqrt(60))

= 0.4814

(C) when n = 150

using normalcdf

setting lower = 16442, upper = 16842, mean = 16642 and sigma = 2400/sqrt(150)

=normalcdf(16842,16442,16642,2400/sqrt(150))

= 0.6926

(D) when n = 400

using normalcdf

setting lower = 16442, upper = 16842, mean = 16642 and sigma = 2400/sqrt(400)

=normalcdf(16842,16442,16642,2400/sqrt(400))

= 0.9044