Question

When attending a movie, patrons are interested in avoiding the pre-movie trivia games, ads, and previews. It is known that the previews begin at the scheduled movie start time and they last between 5 and 15 minutes. Assume that the time of the previews is uniformly distributed. What is the probability that on a given day the previews last between 10 and 12 minutes

Answer 1

0.2 = 20% probability that on a given day the previews last between 10 and 12 minutes

Explanation:

A distribution is called uniform if each outcome has the same probability of happening.

The uniform distributon has two bounds, a and b, and the probability of finding a value between c and d is given by:

`P(c \leq X \leq d) = (d - c)/(b - a)`

It is known that the previews begin at the scheduled movie start time and they last between 5 and 15 minutes.

This means that
`a = 5, b = 15`

What is the probability that on a given day the previews last between 10 and 12 minutes?

`P(10 \leq X \leq 12) = (12 - 10)/(15 - 5) = (2)/(10) = 0.2`

0.2 = 20% probability that on a given day the previews last between 10 and 12 minutes