真係好難的maths question

用戶10960

2009-12-17 3:32 am

The owner of a company that operates a fixed green minibus route
wishes to study the daily mileage of the company’s 42 minibuses. From
past experience, the distribution of the daily mileage is normally
distributed with a mean of 168 km and a standard deviation of 86 km. On
a particular day, a sample of six minibuses is chosen randomly and the
corresponding mileage is recorded.
a What is the mean and standard deviation of the sample mean?

b What is the probability that the average daily mileage of these six
minibuses is between 150 and 200?

回答 (1)

用戶9112

2009-12-17 5:36 am

✔ 最佳答案

(a) The mean of the sample mean = 168km
The standard deviation of the sample mean = 86/√6 = 35.11km
(b) z-score for 150 = (150 - 168)/35.11 = -0.5127
z-score for 200 = (200 - 168)/35.11 = 0.9114
Pr(150 < x < 200)
= Pr(-0.5127 < z < 0.9114)
= 0.5149

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