statistics題目

[匿名]

2012-11-19 6:11 pm

1) In a certain country, the times it takes college students to get up in the morning is believed to be modelled by a normal distribution with a mean of 26.4 minutes and a standard deviation of 3.7 minutes.

a. ‘Very slow’ is used to describe college students who take more than 1.645 standard deviations above the mean to get up in the morning. Find the probability that fewer than 3 students from a random sample of 8 students are ‘very slow’.

2) A fisherman has caught 16 fish of which 3 are undersized. A random sample of 3 is drawn without replacement by the local ranger. If there is more than one undersized fish in the sample the fisherman is fined. What are the chances of the fisherman being fined?

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回答 (1)

用戶25975

2012-11-19 6:26 pm

✔ 最佳答案

1) With P(z > 1.645) = 0.05, the probability that a student being "very slow" is 0.05

So when taking 8 students randomly, prob. that fewer than 3 students being "very slow" is:

0.958 + 8C1 x 0.05 x 0.957 + 8C2 x 0.052 x 0.956 = 0.9942

2) When taking 3 out of 16 randomly:

P(no undersized) = 13/16 x 12/15 x 11/14 = 143/280

P(1 undersized) = 3 x (3 x 13 x 12)/(16 x 15 x 14) = 39/100

So the chance of being fined = 1 - 143/280 - 39/100 = 139/1400

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