Suppose the time between buses at a particular stop is apositively skewed random variable with an average of 60 minutes andstandard deviation of 6 minutes. Suppose the time between buses atthis stop is measured for a randomly selected week, resulting in arandom sample of n = 36 times. The average of this sample,
X, is a random variable that comes from a specific probabilitydistribution.
(a)Which of the following is true about the distribution of meantimes for n = 36?
The distribution will be normally distributed with a mean of 60minutes and a standard deviation of 6 minutes.
The distribution will be positively skewed with a mean of 60minutes and a standard deviation of 6minutes.  Â
The distribution will be normally distributed with a mean of 60minutes and a standard deviation of 1 minutes.
The distribution will be positively skewed with a mean of 60minutes and a standard deviation of 1 minutes.
(b) Calculate the probability the mean time for the sample of 36buses will be between 59 minutes and 61 minutes.
P(59 ≤ X ≤ 61)
=Â Â
(c) How likely is it the average time will exceeds 61 minutes?
P(X ≥ 61)
=
You may need to use the z table to complete this problem.
