Question

Suppose a geyser has a mean time between eruptions of 91 minutes91 minutes. If the interval of time between the eruptions is normally distributed with standard deviation 28 minutes28 minutes​, answer the following questions. ​(a) What is the probability that a randomly selected time interval between eruptions is longer than 103103 ​minutes?

Answer 1

0.3341 is the probability that a randomly selected time interval between eruptions is longer than 103 ​minutes.

Explanation:

We are given the following information in the question:

Mean, μ = 91 minutes

Standard Deviation, σ = 28 minutes

We are given that the distribution of time between the eruptions is a bell shaped distribution that is a normal distribution.

Formula:

`z_(score) = \displaystyle(x-\mu)/(\sigma)`

a) P( time interval between eruptions is longer than 103 ​minutes)

P(x > 103)

`P( x > 103) = P( z > \displaystyle(103 - 91)/(28)) = P(z > 0.4286)`

`= 1 - P(z \leq 0.4286)`

Calculation the value from standard normal z table, we have,

`P(x >103) = 1 - 0.6659 = 0.3341 = 33.41\%`

0.3341 is the probability that a randomly selected time interval between eruptions is longer than 103 ​minutes.