Question

The proportion of students who own a cell phone on college campuses across the country has increased tremendously over the past few years. It is estimated that approximately 90% of students now own a cell phone. Fifteen students are to be selected at random from a large university. Assume that the proportion of students who own a cell phone at this university is the same as nationwide. Let X= the number of students in the sample of 15 who own a cell phone.

Required:
What is the appropriate distribution for X?

Answer 1

Binomial, with
`p = 0.9, n = 15`

Explanation:

For each student, there are only two possible outcomes, either they own a cellphone, or they do not. The probability of a student in the sample owning a cellphone is independent of whether other students own a cellphone or not. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution:

Probability of exactly x sucesses on n repeated trials, with p probability.

90% of students now own a cell phone.

This means that
`p = 0.9`

Fifteen students are to be selected at random from a large university.

This means that
`n = 15`

What is the appropriate distribution for X?

Binomial, with
`p = 0.9, n = 15`