The number of wooden sailboats constructed per month in a smallshipyard is a random variable that obeys the probabilitydistribution given in Table below: Probability distribution ofmonthly Number of Sailboats /Probability( 2 is the sailboat and0.15 is probability; likewise please consider in this way for therest of the data) 2, 0.15; 3, 0.20; 4, 0.30; 5, 0.25; 6, 0.05;7,0.05; Suppose that the sailboat builders have fixed monthly costsof $30,000 and an additional construction cost of $4,800 per boat.(a) Compute the mean and standard deviation of the number of boatsconstructed each month. (b) What is the mean and standard deviationof the monthly cost of the sailboat construction operation? 4 (c)How do your answers in part (b) change if the fixed monthly costincreases from $30,000 to $53,000? Try to compute your answer usingthe results of the calculation in part (b) only. (d) How do youranswers in part (b) change if the construction cost per boatincreases from $4,800 to $7,000, but the fixed monthly cost staysat $30,000? Try to compute your answer using the results of thecalculations of parts (a) and (b) only.
