A study is planned to estimated the proportion of business started in the
year 2000 that had failed within five years of their startup. How large a
sample size is needed to guarantee estimating this proportion correct to
within (18%)
(1) 0.10 with probability 0.95? (4%)
(2) 0.05 with probability 0.95? (4%)
(3) 0.05 with probability 0.99? (4%)
(4) Compare sample sizes for parts (1)~(3), and summarize the effects of
decreasing the margin of error and increasing the confidence level. (6%)
A fast-food restaurant finds that its daily profits have a normal
distribution with mean US$140 and standard deviation US$80.
(1) Find the probability that the restaurant loses money on a given day.
(6%)
(2) Find the probability that the restaurant makes money for the next
seven days in a row. State the probability distribution that you apply
for this. (9%)
John, Mary, and Jane fill orders in a restaurant. John incorrectly fills 15%
of the orders he takes. Mary correctly fills 75% of the orders she takes, and
Jane incorrectly fills 10% of the order she takes. John fills 30% of all orders,
and Mary fills 40% of all orders. 600 orders are filled. Answer the following
questions. (20%)
(1) How many incorrect orders does John fill? (4%)
(2) If the order was filled by Jane, what is the probability that it was filled
incorrectly? (4%)
(3) If the order was filled incorrectly, what is the probability that John fill
it? (6%)
(4)If the order was filled correctly, what is the probability that Mary fills it?
(6%)
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