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. Size of donation $0 $10 $25 $50 Proportion of calls 0.45 0.30 0.20 0.05 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)?

Answer 1

You would expect 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

most common value of x in this population =0

c)P(X>=25) =0.20+0.05 =0.30

d)P(x > 0) =0.30+0.2+0.05=0.55