statistic問題~~

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Question 1 (13 marks)

A company has two production lines to produce leather wallets for
export. Production line A produces 40% of the total output. However, an
average of 15 wallets in every 1,000 produced by production line A are
found to be not within the required standard. Production line B produces
60% of the total output with an average of 12 wallets in every 1,000
being not within the required standard.

a. What is the probability that a wallet randomly selected from
production line A is not within the required standard? (3 marks)

b. What is the probability that a randomly selected wallet is not within
the required standard? (3 marks)

c. If a randomly selected wallet is not within the required standard,
what is the probability that it is produced by production line B?
(3 marks)

d. Construct a probability tree to display all the conditional probabilities
and the joint probabilities involved with respect to the above
situation. (You are not required to put down the numerical value of
the probabilities in the tree.) (4 marks)


Question 2 (14 marks)

BX Airlines Ltd has reported that on average only 5% of its flights are
unable to arrive at the destination on time. Use the Poisson distribution to
approximate the probability that:

a. among the next 50 flights, exactly three of them will be unable to
arrive at the destination on time. (4 marks)

b. among the next 50 flights, more than two flights will be unable to
arrive at the destination on time. (5 marks)

c. Repeat part (a) using Excel. You are required to submit a computer
printout of the relevant Excel spreadsheet that contains the
corresponding input function (with specified values for each of the
parameters) together with the output figure. (5 marks)