maths question ....

2009-12-16 2:58 am

The general manager of a digital products manufacturer believes that
65% of all potential customers prefer to buy MP3 players with over 8GB
built-in memory. A random sample of 100 customers was chosen.
a If the general manager’s belief is true, what is the mean and the
standard deviation of the sample proportion of customers who prefer
to buy MP3 players with over 8GB built-in memory?
b If the general manager’s belief is true, what is the probability that the
sample proportion of customers who prefer to buy MP3 players with
over 8GB built-in memory is less than 0.75?

回答 (1)

用戶9112

2009-12-16 4:31 am

✔ 最佳答案

The proportion of customers who prefer over 8GB = 0.65
The proportion of customers who do not prefer over 8GB = 0.35
(a) Mean number of customers among 100 who prefer over 8GB
= 0.65
Standard deviation = √(0.65*0.35/100) = 0.04770
(b) By central limit theorem, we can use normal distribution to approximate the probability.
z score for 0.75 = (0.75 - 0.65)/0.04770 = 2.097
Pr(z < 2.097) = 0.982

2009-12-15 20:42:16 補充：
(a) Mean number of customers among 100 who prefer over 8GB
should be
(a) Mean proportion of customers who prefer over 8GB

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