4.20 Forest Green Brown, Inc., produces bags of cypress mulch. The weight in pounds per bag varies, as indicated in the accompanying table.

Weight in pounds 44 45 46 47 48 49 50 Proportion of bags 0.04 0.13 0.21 0.29 0.20 0.10 0.03

a. Graph the probability distribution.

b. Calculate and graph the cumulative probability distribution.

c. What is the probability that a randomly chosen bag will contain more than 45 and less than 49 pounds of mulch (inclusive)?

d. Two packages are chosen at random. What is the probability that at least one of them contains at least 47 pounds?

e. Compute—using a computer—the mean and standard deviation of the weight per bag.

f. The cost (in cents) of producing a bag of mulch is 75 + 2X, where X is the number of pounds per bag. The revenue from selling the bag, regardless of weight, is $2.50. If profit is defined as the difference between revenue and cost, find the mean and standard deviation of profit per bag.