Question

A geyser erupts every 25 minutes. A hiker has not consulted a schedule before heading to see the geyser, so the amount of time he spends waiting to see an eruption follows a uniform distribution. What is the probability that he will wait longer than 6 minutes? Give your answer to two decimal places.

Answer 1

0.76 = 76% probability that he will wait longer than 6 minutes

Explanation:

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

The uniform distribution has two bounds, a and b, and the probability of finding a value higher than x is given by:

`P(X > x) = (b - x)/(b - a)`

A geyser erupts every 25 minutes. A hiker has not consulted a schedule before heading to see the geyser, so the amount of time he spends waiting to see an eruption follows a uniform distribution.

This means that
`a = 0, b = 25`

What is the probability that he will wait longer than 6 minutes?

`P(X > 6) = (25 - 6)/(25 - 0) = 0.76`

0.76 = 76% probability that he will wait longer than 6 minutes