Chapter 7.2, Problem 26E

The superintendent of a large school district, having once had a course in probability and statistics, believes that the number of teachers absent on any given day has a Poisson distribution with parameter μ. Use the accompanying data on absences for 50 days to obtain a large-sample CI for μ. [Hint: The mean and variance of a Poisson variable both equal μ, so

$Z=\frac{\bar{X}-\mu }{\sqrt{\mu /n}}$

has approximately a standard normal distribution. Now proceed as in the derivation of the interval for p by making a probability statement (with probability 1 − α) and solving the resulting inequalities for μ — see the argument just after (7.10).]

Number of absences	0	1	2	3	4	5	6	7	8	9	10
Frequency	1	4	8	10	8	7	5	3	2	1	1