When a production process is operating correctly, the number of units produced per hour has a normal distribution with a mean of 105 and a standard deviation of 20. A random sample of 25 different hours was taken.
a. Find the mean of the sampling distribution of the sample means.
b. Find the variance of the sampling distribution of the sample mean.
c. Find the standard error of the sampling distribution of the sample mean.
d. What is the probability that the sample mean exceeds 106 units?