The probability that a truck will be going over the speed limit on I-77 South between Dobson and Elkin is about 75%. Suppose a random sample of five trucks are observed on this stretch of I-77.
a. Find the mean of this probability distribution. Show the formula and your work.
b. Interpret the mean in the context of the problem.
c. Find the standard deviation of this probability distribution. Round your answer to 2 decimal places.
d. Find the probability that exactly 3 of the observed trucks are speeding.
e. Find the probability that less than 3 of the observed trucks are speeding.