Question: Suppose the average speeds of passenger trains traveling from Newark, New Jersey, to Philadelphia, Pennsylvania, are normally distributed, with a mean average speed of 88 miles per hour and a standard deviation of 6.4 miles per hour.

a. What is the probability that a train will average more than 80 miles per hour?

b. What is the probability that a train will average between 90 and 100 miles per hour?

c. Find an average speed such that the probability of more than that speed is .08.

d. Suppose the mean average speed is unknown but a standard deviation is known to be 5 miles per hour. What is the value of the mean average speed if there is 30% chance that a train will average greater than 96 miles per hour?