A test was done to look at the maximum speed of mopeds. They found that the maximum speed had a normal distribution with a mean of 29 mph and standard deviation of 1.4 mph. Consider randomly selecting a moped.
a. What is the probability that the maximum speed is at most 31 mph?
b. What is the probability that the maximum speed is at least 29.8 mph?
c. What is the probability that maximum speed differs from the mean value by at most 1.5 standard deviations?
d. Suppose we select 49 mopeds, what is the probability that the sample mean will be at least 29.5 mph?