Suppose a geyser has a mean time betwen eruptions of 96 minu

Suppose a geyser has a mean time betwen eruptions of 96 minutes.  Let the interval of time between the erupitons be normally distributed with standard deviation 29 minutes.

a. what is the probability that a randomly selected time interval between eruptions is longer than 108 minutes?

b. what is the probability that a random sample of 9 time intervals between eruptions has a mean longer than 108 minutes?

c. what is the probability that a random sample of 39 time intervals between eruptions has a mean longer than 108 minutes?

d. the probability that the mean of a random sample of 39 time intervals is more than 108 miniutes is approximatley what?

Solution

We need to calculate Z scores and use the Z table to find probabilities.

Step 1: P(X>108)=(108-96)/29= .4138

P=.3409

Step 2: Since we are given a sample of 9, we need to divide the standard deviation by sqrt(9)

P(X>108)=(108-96)/(29/sqrt(9))=1.24

P=.1075

Step 3: Same as above, but with a sample of 39.

P(X>108)=(108-96)/(29/sqrt(39))=2.58

P=.0049

Step 4: Same as step 3 just worded different.

P=.0049

Hope this helps! :) Let me know if you have any other questions.