The engine of a spaceship runs for a time T (seconds) and it causes the acceleration a : 2 111/ 52. The distance travelled during acceleration is X : aTg. The time T is a continuous random variable uniformly distributed in the interval I : [100, 150] (seconds). a. Calculate the expected value of the distance travelled. Calculate the probability that the distance is more than 20 000 meters. C. ) b.) ) Calculate the standard deviation of the distance. d.) Ten similar spaceships are sent, and their engines are run for times T1, . . . ,Tm, which are independent and uniformly distributed over the same interval I . Calculate the probability that exactly three of the ships travel more than 20 000 meters during the acceleration