Suppose that fund-raisers at a university call recent graduates to request donat

Question

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.

Three attempts were made to contact each graduate. A donation of $0 was recorded both for those who were contacted but who declined to make a donation and for those who were not reached in three attempts. Consider the variable

x = amount

of donation for the population of last year's graduates of this university.

(a)

Write a few sentences describing what you think you might see if the value of x was observed for each of 1000 graduates.

You would expect roughly  of the graduates to donate nothing, roughly  to donate $10, roughly  to donate $25, and roughly  to donate $50. The 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?

$

(c)

What is

P(x 25)?

(d)

What is

P(x > 0)?

Explanation / Answer

You would expect roughly 450 of the graduates to donate nothing, roughly 300 to donate $10, roughly 200 to donate $25, and roughly 50 to donate $50. The frequencies would be close to, but not exactly, these values. The four frequencies would add to 1000 .

b)most common value of x in this population : $0 (due to highest probability

c)P(x 25) =P(X=25)+P(X=50) =0.2+0.05 =0.25

d)P(X>0) =P(X=10)+P(X=25)+P(X=50) =0.30+0.20+0.05 =0.55

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