Let x be a random variable that represents the speed of the first vehicle passing an observation point between 11am to 12n on a remote highway, automatically recorded by a police radar. Based on past recording over many days, the random variable has an approximate normal distribution with a mean of 72 mph and a standard deviation of 5 mph.
a) What is the probability that, on the next day, the speed of the first vehicle passing the observation point between 11am to 12n is less than 65 mph?
b) What is the probability that, on the next day, the speed of the first vehicle passing the observation point between 11am to 12n is greater than 75mph?
c) What is the probability that, on the next day, the speed of the first vehicle passing the observation point between 11am to 12n is between 65mph and 75mph?
d) On 80% of the days in the coming tear, the sped of the first vehicle passing the observation point between 11am to 12n will be below what value?
e) On each day of the next week from M-F, the sped of the first vehicle passing the observation point between 11am to 12n will be recorded. What is the probability that the average speed of these 5 recordings is more than 70mph?