The Internal Revenue Service is studying the category of charitable contributions. A sample of 34 returns is selected from young couples between the ages of 20 and 35 who had an adjusted gross income of more than $100,000. Of these 34 returns, 8 had charitable contributions of more than $1,000. Suppose 7 of these returns are selected for a comprehensive audit. a. Explain why the hypergeometric distribution is appropriate. Because you are sampling a small population without replacement. O you are sampling a small population with replacement. O you are sampling a large population without replacement. b. What is the probability exactly one of the seven audited had a charitable deduction of more than $1,000? (Round your answer to 4 decimal places.) Probability c. What is the probability at least one of the audited returns had a charitable contribution of more than $1,000? (Round your answer to 4 decimal places.) Probability
The Internal Revenue Service is studying the category of charitable contributions. A sample of 34 returns is selected from young couples between the ages of 20 and 35 who had an adjusted gross income of more than $100,000. Of these 34 returns, 8 had charitable contributions of more than $1,000. Suppose 7 of these returns are selected for a comprehensive audit. a. Explain why the hypergeometric distribution is appropriate. Because you are sampling a small population without replacement. O you are sampling a small population with replacement. O you are sampling a large population without replacement. b. What is the probability exactly one of the seven audited had a charitable deduction of more than $1,000? (Round your answer to 4 decimal places.) Probability c. What is the probability at least one of the audited returns had a charitable contribution of more than $1,000? (Round your answer to 4 decimal places.) Probability
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![**Title: IRS Study on Charitable Contributions: Probability Analysis**
The Internal Revenue Service is examining the category of charitable contributions. A sample of 34 tax returns has been selected from young couples between the ages of 20 and 35, all of whom have an adjusted gross income exceeding $100,000. Out of these 34 returns, 8 exhibited charitable contributions greater than $1,000. Suppose 7 of these returns are chosen for a meticulous audit.
**a. Explanation for Hypergeometric Distribution**
To determine why the hypergeometric distribution is suitable, consider the following:
- You are sampling a small population without replacement.
(Option selected: • you are sampling a small population without replacement.)
**b. Probability of Exactly One Audited Return Exceeding $1,000**
Calculate the probability that exactly one of the seven audited returns showed a charitable deduction of more than $1,000. Ensure your answer is rounded to four decimal places.
\[ \text{Probability:} \, \_\_\_\_ \]
**c. Probability of At Least One Audited Return Exceeding $1,000**
Determine the probability that at least one of the audited returns had a charitable contribution of more than $1,000. Ensure your answer is rounded to four decimal places.
\[ \text{Probability:} \, \_\_\_\_ \]
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Transcribed Image Text:**Title: IRS Study on Charitable Contributions: Probability Analysis**
The Internal Revenue Service is examining the category of charitable contributions. A sample of 34 tax returns has been selected from young couples between the ages of 20 and 35, all of whom have an adjusted gross income exceeding $100,000. Out of these 34 returns, 8 exhibited charitable contributions greater than $1,000. Suppose 7 of these returns are chosen for a meticulous audit.
**a. Explanation for Hypergeometric Distribution**
To determine why the hypergeometric distribution is suitable, consider the following:
- You are sampling a small population without replacement.
(Option selected: • you are sampling a small population without replacement.)
**b. Probability of Exactly One Audited Return Exceeding $1,000**
Calculate the probability that exactly one of the seven audited returns showed a charitable deduction of more than $1,000. Ensure your answer is rounded to four decimal places.
\[ \text{Probability:} \, \_\_\_\_ \]
**c. Probability of At Least One Audited Return Exceeding $1,000**
Determine the probability that at least one of the audited returns had a charitable contribution of more than $1,000. Ensure your answer is rounded to four decimal places.
\[ \text{Probability:} \, \_\_\_\_ \]
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**Help Section:**
For additional assistance or clarification on calculations, please refer to our statistical guides or contact a math tutor through our educational resource network.
Expert Solution
Step 1
The question is about discrete probability distribution
Given :
Sample no. of returns selected from young couples ( N ) = 34
No. of returns selected for a comprehensive audit ( n ) = 7
No. of returns has charitable contribution from N ( r ) = 8
To find :
a ) Explain why hypergeometric dist. is appropriate
b ) Prob. that exactly 1 of the 7 audited had deduction of more than $1000
c ) Prob. that at least 1 of the 7 audited had contribution of more than $1000
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