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 call 0.40 0.30 0.25 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)?

It's also expected that approximately [tex]1000 \times 0.40 =400[/tex] of both, the students contribute zero, approximately [tex]1000 \times 0.30 =300[/tex] to donors $10, approximately [tex]1000 \times 0.25 = 250[/tex] donors $25, and then about [tex]1000 \times 0.05 = 500[/tex] dollars $50 donors. Its frequencies would be similar to and not precisely, the probability. The four levels will stack up to a thousand.

In point b:

It is the population, in which the key value of x is a $0 donation ( 40 percent of students do this).

In point c:

[tex]\to P(X \geq 25) \\\\\to 0.25+0.05 \\\\\to 0.30[/tex]

In point d:

[tex]\to P(X>0)\\\\ \to 1-P(X=0)\\\\ \to 1- 0.40\\\\\to 0.60\\\\[/tex]