Easy probability question

[cb]

Main Question or Discussion Point

Here's the question:

A quality-control engineer samples 100 items manufactured by a certain process, and finds that 15 of them are defective. True or false:

(a.) The probability that an item produced by this process is defective is 0.15.

(b.) The probability that an item produced by this process id defective is likely to be close to 0.15, but not exactly equal to 0.15.

The book gives the answers False for (a.) and True for (b.).

I understand that since the two events can either be defective or not defective, they are mutually exclusive with equally likely outcomes and therefore:

P(E) = k / N, where k=number of outcomes in event and N=total outcomes

So I calculated that P(defective) = 0.15. Why would it be close but not exactly equal to 0.15?

 

[EnumaElish]

That's because the engineer's estimate is only a statistic. You can define a standard deviation or variance around that statistic. You can also make the statement "with Z% likelihood, the probability of defect is between 0.15-X and 0.15+X." But you may not claim that "the probability of defect is exactly equal to 0.15."