. Suppose that an airline quotes a flight time of 2 hours, 10 minutes between two cities. Furthermore, suppose that historical flight records indicate that the actual flight time between the two cities, x, is uniformly distributed between 2 hours and 2 hours, 20 minutes (uniform distribution). Letting the time unit be one minute,

a. What is the mean?

b. What is the standard deviation?

c. Find P(125 x 135) (between 125 minutes and 135 minutes).

d. Find the probability that a randomly selected flight between the two cities will be at least five minutes late (greater than 2 hours 15 minutes).

e. What is the probability the plane will arrive plus or minus 1 standard deviation away from the mean? (Hint: Calculate the mean and standard deviation. Add the standard deviation to the mean to get plus 1 standard deviation away from the mean and subtract the standard deviation from the mean to get minus 1 standard deviation from the mean. Then use these two numbers as your a and b),