The Superintendent of a Large School District, Having Once Had $\lambda$

Essay

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 $\lambda$ . Use the accompanying data on absences for 50 days to derive a large-sample CI for $\lambda$ . [Hint: The mean and variance of a Poisson variable both equal $\lambda$ , so $Z = ( \bar{X} - \lambda ) / \sqrt { \lambda / n }$ 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 - $\alpha$ ) and solving the resulting inequalities for $\lambda$ . $$\begin{array} { c c c c c c c c c c c c } \hline \text { \#Absences } & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\\hline \text { Frequency } & 1 & 6 & 8 & 10 & 8 & 7 & 5 & 3 & 2 & 1 & 1 \\\hline\end{array}$$