The Wall Street Journal reported 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 $16,434. Assume that the standard deviation is o = $2,961. Use z-table. a. What is the probability that a sample of taxpayers from this income group who have itemized deductions will show a sample mean within $180 of the population mean for each of the following sample sizes: 30, 50, 100, and 400? Round your answers to four decimals. n = 30 n= 50 n = 100 n= 400 b. What is the advantage of a larger sample size when attempting to estimate the population mean? Round your answers to four decimals. A larger sample - sSelect your answer - v the probability that the sample mean will be within a specified distance of the population mean. In the automobile insurance example, the probability of being within ±180 of µ ranges from for a sample of size 30 to| for a sample of size 400.
The Wall Street Journal reported 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 $16,434. Assume that the standard deviation is o = $2,961. Use z-table. a. What is the probability that a sample of taxpayers from this income group who have itemized deductions will show a sample mean within $180 of the population mean for each of the following sample sizes: 30, 50, 100, and 400? Round your answers to four decimals. n = 30 n= 50 n = 100 n= 400 b. What is the advantage of a larger sample size when attempting to estimate the population mean? Round your answers to four decimals. A larger sample - sSelect your answer - v the probability that the sample mean will be within a specified distance of the population mean. In the automobile insurance example, the probability of being within ±180 of µ ranges from for a sample of size 30 to| for a sample of size 400.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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part A
![**The Wall Street Journal** reported 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 $16,434. Assume that the standard deviation is σ = $2,961. Use a z-table.
**a.** What is the probability that a sample of taxpayers from this income group who have itemized deductions will show a sample mean within $180 of the population mean for each of the following sample sizes: 30, 50, 100, and 400? Round your answers to four decimals.
\( n = 30 \)
\[ \]
\( n = 50 \)
\[ \]
\( n = 100 \)
\[ \]
\( n = 400 \)
\[ \]
**b.** What is the advantage of a larger sample size when attempting to estimate the population mean? Round your answers to four decimals.
A larger sample \[ \text{ } \] the probability that the sample mean will be within a specified distance of the population mean. In the automobile insurance example, the probability of being within ±180 of \( μ \) ranges from \[ \text{ } \] for a sample of size 30 to \[ \text{ } \] for a sample of size 400.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc2d28942-f25c-4736-9df7-d70631fb5969%2F31919ddc-e645-49d2-b112-15432ca9ff7f%2F1edjn6v_processed.png&w=3840&q=75)
Transcribed Image Text:**The Wall Street Journal** reported 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 $16,434. Assume that the standard deviation is σ = $2,961. Use a z-table.
**a.** What is the probability that a sample of taxpayers from this income group who have itemized deductions will show a sample mean within $180 of the population mean for each of the following sample sizes: 30, 50, 100, and 400? Round your answers to four decimals.
\( n = 30 \)
\[ \]
\( n = 50 \)
\[ \]
\( n = 100 \)
\[ \]
\( n = 400 \)
\[ \]
**b.** What is the advantage of a larger sample size when attempting to estimate the population mean? Round your answers to four decimals.
A larger sample \[ \text{ } \] the probability that the sample mean will be within a specified distance of the population mean. In the automobile insurance example, the probability of being within ±180 of \( μ \) ranges from \[ \text{ } \] for a sample of size 30 to \[ \text{ } \] for a sample of size 400.
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