Question

Suppose a geyser has a mean time between eruptions of 80 minutes. If the interval of time between the eruptions is normally distributed with standard deviation 26 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 0.3228. ​(Round to four decimal places as​ needed.) ​(b) What is the probability that a random sample of 8 time intervals between eruptions has a mean longer than 92 ​minutes? The probability that the mean of a random sample of 8 time intervals is more than 92 minutes is approximately nothing. ​(Round to four decimal places as​ needed.)

ONLY ANSWER PART B

Answer 1

Solution :

mean = = 80

standard deviation = = 26

b) n = 8

= = 80

= / n = 26 / 8 = 9.19

P( > 92) = 1 - P( < 92)

= 1 - P[( - ) / < (92 - 80) / 9.19 ]

= 1 - P(z < 1.31)

Using z table,    

= 1 - 0.9049

= 0.0951