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The number of wooden sailboats constructed per month in a small shipyard is a random variable with the following probability distribution.
X
2
3
4
5
P(X)
0.4
0.3
0.2
0.1
(a) Suppose the sailboat builders have fixed monthly costs of $25,000 and an additional construction cost of $5,000 per boat. Find the mean and standard deviation of the monthly costs.
(b) Assume that the number of sailboats constructed is independent from month to month. In the next three months, what is the probability that the shipyard produces at least 4 boats per month for two months?
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