Question

Suppose a geyser has a mean time between eruptions of 70 minutes

If the interval of time between the eruptions is normally distributed with standard deviation 20 minutes

answer the following questions.

​(a) What is the probability that a randomly selected time interval between eruptions is longer than

80 ​minutes?

The probability that a randomly selected time interval is longer than 80 minutes is approximately?

Answer 1

Suppose a geyser has a mean time between eruptions of 70 minutes. If the interval of time between the eruptions is normally distributed with standard deviation 20 minutes, answer the following questions.

​(a) What is the probability that a randomly selected time interval between eruptions is longer than 80 minutes?

WE have to find P(X>80)

We are given mean = 70, SD = 20

P(X>80) = 1 – P(X<80)

Z = (X – mean) / SD

Z = (80 – 70)/20

Z = 10/20

Z = 0.50

P(Z<0.50) = P(X<80) = 0.691462

(by using z-table)

P(X>80) = 1 – P(X<80)

P(X>80) = 1 – 0.691462

P(X>80) = 0.308538

Required probability = 0.308538