Question

Suppose a geyser has a mean time between eruptions of 84 minutes. If the interval of time between the eruptions is normally distributed with standard deviation 17 minutes​, answer the following questions. ​(a) What is the probability that a randomly selected time interval between eruptions is longer than 92 ​minutes? The probability that a randomly selected time interval is longer than 92 minutes is approximately nothing. ​(Round to four decimal places as​ needed.)

Answer 1

Solution:

Given: X =  the interval of time between the eruptions is normally distributed with  mean time between eruptions of 84 minutes.and standard deviation 17 minutes​.

Find:

P( X > 92 ) =............?

Find z score for x = 92

thus we get:

P( X > 92 ) = P( Z> 0.47 )

P( X > 92 ) = 1 - P( Z < 0.47 )

Look in z table for z = 0.4 and 0.07 and find corresponding area.

P( Z< 0.47 )= 0.6808

thus

P( X > 92 ) = 1 - P( Z < 0.47 )

P( X > 92 ) = 1 - 0.6808

P( X > 92 ) = 0.3192

The probability that a randomly selected time interval is longer than 92 minutes is approximately 0.3192