Assume the weight of cargo for a company truck follows a uniform distribution ranging between 300 and 450 pounds.

a) What is the expected value of the weight of the cargo?

b) What is the standard deviation of the weight of the cargo?

c) Draw a plot of the pdf.

d) Find the probability that the weight is between 325 and 375 pounds.

e) What is the probability that the cargo’s weight is at least 325 pounds?

f) Suppose that an efficiency study was conducted and found that the probability that the cargo weight is greater than the expected value and less than x is 0.3. Furthermore, weight x should be the maximum weight allowed for cost efficiency. Find what this weight is.