Four secretaries employed by an office file 40, 10, 30 and 20% of the documents. The
probabilities that errors will be made in the process are 0.01, 0.04, 0.06, and 0.10. If a
document was misfiled.
(一) What are the respective probabilities that the document was filed by (1) the first
secretary. (2) the second secretary, (3) the third secretary, and (4) the fourth
secretary? (12%)
(二) Whom would you guess to be the person that filed the misfiled document? And
why? (8%)
Give the definition for each of the following well-known distributions:
(一) Bernoulli trial (4%),
(二) Binomial distribution (4%),
(三) Poisson distribution (4%),
(四) Normal (Gaussian) distribution (4%), and
(五) Exponential distribution. (4%)
Suppose there were 600 pieces of same toy, from which a random sample of 60 pieces
were obtained without replacement. If 6 pieces among the sample are found to be faulty,
find a 95% confidence interval for the faulty rate among all of the 600 pieces. (20%)
A shoe manufacturer wanted to test the strength of two kinds of material, A and B .
The method was to randomly select 8 athletes and have each of the athlete wear a shoe
of material A on one foot and a shoe of material B on the other foot, then measure
the days until that each shoe was worn out. Assume that the following data were
obtained
Assume that each of the material strength has a normal distribution, and the
manufacturer would like to test if the two kinds of material A and B are of the same
strength. Then for the hypothesis testing,
(一) Give the null hypothesis and the alternative (5%)
(二) Give the critical region (rejection region) (5%)
(三) Execute the test and give your conclusion at level of signifance α = 0.05 (10%)
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