Question

Suppose a geyser has a mean time between eruptions of 86 minutes Let the interval of time between the eruptions be normally distributed with standard deviation 26 minutes

.

​(a) What is the probability that a randomly selected time interval between eruptions is longer than 99 ​minutes?

​(b) What is the probability that a random sample of 9 time intervals between eruptions has a mean longer than 99 ​minutes?

Answer 1

Solution :

(a)

P(x > 99) = 1 - P(x < 99)

= 1 - P[(x - ) / < (99 - 86) / 26)

= 1 - P(z < 0.5)

= 1 - 0.6915

= 0.3085

Probability = 0.3085

(b)

= / n = 26 / 9 = 8.6667

P( > 99) = 1 - P( < 99)

= 1 - P[( - ) / < (99 - 86) / 8.6667]

= 1 - P(z < 1.50)

= 1 - 0.9332

= 0.0668

Probability = 0.0668