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Suppose that fund-raisers at a university call recent graduates to request donations for campus outreach programs. They report the following information for last year's graduates. Size of donation Proportion of calls 0.40 $0 $10 $25 $50 (c) What is P(x ≥ 25)? 0.30 0.25 Three attempts were made to contact each graduate. A donation of $0 was recorded both for those who were contacted but declined to make a donation and for those who were not reached in three attempts. Consider the variable x = amount of donation for a person selected at random from the population of last year's graduates of this university. (a) Write a few sentences describing what donation amounts you would expect to see if the value of x was observed for each of 1,000 graduates. to donate $25, and roughly (d) What is P(x > 0)? 0.05 You would expect roughly of the graduates to donate nothing, roughly frequencies would be close to, but not exactly, these values. The four frequencies would add to (b) What is the most common value of x in this population? to donate $10, roughly to donate $50. The

Suppose that fund-raisers at a university call recent graduates to request donations for campus outreach programs. They report the following information for last year's graduates. Size of donation Proportion of calls 0.40 $0 $10 $25 $50 (c) What is P(x ≥ 25)? 0.30 0.25 Three attempts were made to contact each graduate. A donation of $0 was recorded both for those who were contacted but declined to make a donation and for those who were not reached in three attempts. Consider the variable x = amount of donation for a person selected at random from the population of last year's graduates of this university. (a) Write a few sentences describing what donation amounts you would expect to see if the value of x was observed for each of 1,000 graduates. to donate $25, and roughly (d) What is P(x > 0)? 0.05 You would expect roughly of the graduates to donate nothing, roughly frequencies would be close to, but not exactly, these values. The four frequencies would add to (b) What is the most common value of x in this population? to donate $10, roughly to donate $50. The

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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### University Fund-Raising Data Analysis Fundraisers at a university contacted recent graduates to request donations for campus outreach programs. They gathered the following data regarding last year's graduates: #### Donation Data | Size of Donation | $0 | $10 | $25 | $50 | |------------------|------|-----|-----|-----| | Proportion of Calls | 0.40 | 0.30 | 0.25 | 0.05 | #### Donation Distribution Analysis Three attempts were made to contact each graduate. A donation of $0 was recorded both for those who were contacted but declined to make a donation and for those who were not reached in three attempts. Let \( x \) represent the amount of donation for a person selected at random from the population of last year's graduates of this university. **(a) Expected Donation Amounts:** You would expect roughly [Blank 1] of the graduates to donate nothing, roughly [Blank 2] to donate $10, roughly [Blank 3] to donate $25, and roughly [Blank 4] to donate $50. The frequencies would be close to, but not exactly, these values. The four frequencies would add to [Blank 5]. **(b) Most Common Value of \( x \):** What is the most common value of \( x \) in this population? $ [Blank 6] **(c) Probability of Donation \( \geq 25 \):** What is \( P(x \geq 25) \)? [Blank 7] **(d) Probability of Donation \( > 0 \):** What is \( P(x > 0) \)? [Blank 8] ### Explanation: 1. **Expected Donation Amounts Calculation:** - Roughly 40% of the graduates are expected to donate $0. - Roughly 30% of the graduates are expected to donate $10. - Roughly 25% of the graduates are expected to donate $25. - Roughly 5% of the graduates are expected to donate $50. 2. **Most Common Value of \( x \):** - The most common donation value (mode of the distribution) would be $0, as the highest proportion of calls resulted in no donation (40%). 3. **Probability Calculation of \( x \geq 25 \):** - \( P(x \geq 25) =
Transcribed Image Text:### University Fund-Raising Data Analysis Fundraisers at a university contacted recent graduates to request donations for campus outreach programs. They gathered the following data regarding last year's graduates: #### Donation Data | Size of Donation | $0 | $10 | $25 | $50 | |------------------|------|-----|-----|-----| | Proportion of Calls | 0.40 | 0.30 | 0.25 | 0.05 | #### Donation Distribution Analysis Three attempts were made to contact each graduate. A donation of $0 was recorded both for those who were contacted but declined to make a donation and for those who were not reached in three attempts. Let \( x \) represent the amount of donation for a person selected at random from the population of last year's graduates of this university. **(a) Expected Donation Amounts:** You would expect roughly [Blank 1] of the graduates to donate nothing, roughly [Blank 2] to donate $10, roughly [Blank 3] to donate $25, and roughly [Blank 4] to donate $50. The frequencies would be close to, but not exactly, these values. The four frequencies would add to [Blank 5]. **(b) Most Common Value of \( x \):** What is the most common value of \( x \) in this population? $ [Blank 6] **(c) Probability of Donation \( \geq 25 \):** What is \( P(x \geq 25) \)? [Blank 7] **(d) Probability of Donation \( > 0 \):** What is \( P(x > 0) \)? [Blank 8] ### Explanation: 1. **Expected Donation Amounts Calculation:** - Roughly 40% of the graduates are expected to donate $0. - Roughly 30% of the graduates are expected to donate $10. - Roughly 25% of the graduates are expected to donate $25. - Roughly 5% of the graduates are expected to donate $50. 2. **Most Common Value of \( x \):** - The most common donation value (mode of the distribution) would be $0, as the highest proportion of calls resulted in no donation (40%). 3. **Probability Calculation of \( x \geq 25 \):** - \( P(x \geq 25) =
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