Question
In: Statistics and Probability
The Wall Street Journal reports that 33% of taxpayers with adjusted gross incomes between $30,000 and...
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
Solutions
Expert Solution
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
orchestra answered 2 years agoRelated Solutions
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