Question

1. The number of wooden sailboats constructed per month in a small shipyard is a random variable that obeys the probability distribution given in the table below.

Suppose that the sailboats builders have fixed monthly costs of 30.000€ and an additional construction cost of 4.800€ per boat.

Number of sailboats xi

Probability pi

2

0.15

3

0.20

4

0.30

5

0.25

6

0.05

7

0.05

1. Compute the mean and standard deviation of the number of boats constructed each month.
2. What is the mean and standard deviation of the monthly cost of the sailboat construction operation?
3. How do your answer in part (b) change if the fixed monthly cost increases from 30.000€ to 53.000€? Try to compute your answer using the result of the calculation in part (b) only.

Answer 1

From the table,

1).Mean =$x*p$

0.3,0.6,1.2,1.25,0.3,0.35

standard deviation =$\sqrt{variance}$

variance= x²*p

0.6,1.8,4.8,6.25,1.8,2.45

2).monthly cost of sail boats

for mean

=30+4.8*mean

31.44,32.88,35.76,36,31,44,31,68

standard deviation

=30+4.8* standard deviation

33.718,36.4398,40.5163,42,36.4398,37.513

3)monthly cost given that 50 is fixed and 4.8 per cost.

mean =50+4.8*mean

51.44,52.88,88.76,56,51.44,51.68

standard deviation =50+4.8* standard deviation

53.718,56.4398,60.516,62,56.439,57.513