Solve the following problem:
Q: Some Japanese consumers are willing to pay premium prices for Maine lobsters. One factor in the high cost is the mortality rate during the long distance shipping from Maine to Japan. Suppose the number of deaths x per 10 lobsters is given by the following distribution. An air shipment of 750 crates, each containing 10 lobsters, is sent from Bangor, Maine to Tokyo (Blaisdell, 1998).
X p(x) xP(x)
0 0.48
1 0.28
2 0.14
3 0.06
4 0.03
5 0.01
Sum:
a. Is this a valid probability distribution? Why or why not? Please be sure to thoroughly justify your answer.
b. What is the probability that a randomly selected crate has no dead lobsters? Explain briefly.
c. What is the probability that a randomly selected crate has at least one dead lobster in it?
d. The mean of a discrete distribution is found using the formula u= xP(x). Fill in the column of the table above by multiplying each value for x by its probability. Add up these values to find the mean of this probability distribution. Write the mean below.
e. Using the value you found for the mean above, how many lobsters would we expect to be dead in the entire shipment of 750 crates? Explain.
f. Would it be unusual for a randomly selected crate to contain no dead lobsters? Explain briefly.