Suppose that the time it takes Taylor to make one of the Commes des Mouflons jackets is in fact variable and uniformly distributed between 2.25 and 3.5 hours for each jacket.

Questions:

a. Draw a graph of the distribution of "T", the amount of time it takes Taylor to make a jacket. Make sure to notate the density! b. What is the probability that it will take Taylor LESS than 3 hours to make the next jacket? c. What is the probability that it will take Taylor MORE than 2.5 hours to make the next jacket? d. What is the probability that it will take Taylor EXACTLY 3 hours to make the next jacket? e. How long should Taylor EXPECT to take to make the next jacket? f. What is the standard deviation of the variable "T"? g. Suppose that in May and June combined Commes des Mouflons receives 37 orders for jackets. Taylor estimates that she can spare a total of 100 hours to make these jackets without it cutting into her other business. How many hours can she spare for EACH jacket? h. Describe the distribution of the EXPECTED number of hours Taylor will need to spend making EACH of the 37 jackets ordered in May and June. Include the mean, standard deviation AND the shape of the distribution. i. Using your calculations from parts g and h, what is the probability that Taylor will be able to finish the 37 jackets without it cutting into her other business?