Question

If six hundred confidence intervals, each having a level of confidence of 95%, were computed for a population mean, µ, approximately how many of the intervals would be expected to contain µ?

Answer 1

Since, the confidence level of each confidence interval is 95%, each confidence interval contains the population mean, µ, with probability equal to 95% = 0.95.

Now, let X denote the number of confidence intervals, out of 600 confidence intervals, which contain µ.

Since, there is a fixed number of confidence intervals (equal to 600), each confidence interval has two outcomes (containing µ or not containing µ) and each confidence interval contains µ with probability 0.95 independent of other confidence intervals, thus we can conclude that:
X ~ Binomial(n = 600, p = 0.95)

Thus, the expected number of confidence intervals which contain µ is given by:
E(X) = np [Using the formula for mean of a Binomial Distribution]

= 600*0.95

= 570 [ANSWER]

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