Question

Exactly 20% of the students in a school wear glasses. Sixty-five students are randomly selected to determine the probability that exactly 10 students wear glasses. Should a binomial probability density function or a cumulative distribution function be used? Explain.

A binomial cumulative distribution function should be used because the question asks for determining the probability that exactly 10 students wear glasses.
A binomial probability density function should be used because the question asks for determining the probability that exactly 10 students wear glasses.
A binomial cumulative distribution function should be used because the question states exactly 20% of students wear glasses.
A binomial probability density function should be used because the question states exactly 20% of the students wear glasses.
A binomial probability would not be used because the events are not independent of each other.

Answer 1

A binomial probability density function should be used because the question asks for determining the probability that exactly 10 students wear glasses.

Explanation:

A binomial probability density function is used when we want to know the probability of an exact value.

A cumulative distribution function is used when we want to know the probability of less than or equal to a value.