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

a.

You would expect roughly 1000*.40 = 400 of the graduates to donate nothing, roughly 1000*.30 =300 to donate $10, roughly 1000*.25 = 250 to donate $25, and roughly 1000*.05 = 50 to donate $50. The frequencies would be close to the probabily distribution, but not exactly, these values. The four frequencies would add to 1000.

b. The most common value of x in this population is a $0 donation ( 40% of students do this)

c. P(X>=25) = .25+.05 = .30

d. P(X>0) = 1-P(X=0) = 1-.40 = .60

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