In: Math
Suppose a geyser has a mean time between eruptions of 66 minutes. If the interval of time between the eruptions is normally distributed with standard deviation
24 minutes, answer the following question.
What is the probability that a random sample of 38 time intervals between eruptions has a mean longer than 76 minutes?
The probability that the mean of a random sample of 38 time intervals is more than 76 minutes is approximately __________
(Round to four decimal places as needed.)
Solution :
Given that ,
mean = = 66
standard deviation = = 24
n = 38
= = 66 and
= / n = 24 / 38 = 3.8933
P( > 76) = 1 - P( < 76)
= 1 - P(( - ) / < (76 - 66) / 3.8933)
= 1 - P(z < 2.95)
= 1-0.9984 Using standard normal table.
Probability = 0.0016
The probability that the mean of a random sample of 38 time intervals is more than 76 minutes is approximately 0.0016.