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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? Please be sure to show your work and to answer the question.

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.

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Japanese consumers willing to pay premiums prices for Maine lobster is discussed.

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1. 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.
Yes, it is a ...

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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