Question

Hypergeometric distribution- Practical Example

Suppose that a technology task force is being formed to study technology awareness among instructors. Assume that ten people will be randomly chosen to be on the committee from a group of 28 volunteers, 20 who are technically proficient and eight who are not. We are interested in the number on the committee who are not technically proficient. Find the probability that five on the committee are not technically proficient.

Step1. In words, define the random variable X.

Step2. List the values that X may take on.

Step3. How many instructors do you expect on the committee who are not technically proficient?

Find value of p, N, n, r from the question.

Step4. Find the probability that five on the committee are not technically proficient.

Answer 1

Solution:

Step 1:

x: Random variable: number on the committee who are not technically proficient

Step 2:

values that X may take on, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

Step 3: Instructor is interested to find probability that 5 committee who are not technically proficient.

We are given,

Sample_size (x)	5
Number_sample(n)	10
Population_size( r )	8
Number_population(N)	28

Step 4:

We have to Find the probability that five on the committee are not technically proficient

P( x = 5 ) = ____________ ?

Using excel,

=HYPGEOM.DIST(5,10,8,28,FALSE)

P( x = 5 ) = 0.0662

Done