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# maths question ....

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?

### 1 Answer

- 自由自在Lv 71 decade agoFavorite Answer
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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