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

question 30

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 $\lambda$ . $$\begin{array} { c c c c c c c c c c c c } \hline \text { \#Absences } & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\\hline \text { Frequency } & 1 & 6 & 8 & 10 & 8 & 7 & 5 & 3 & 2 & 1 & 1 \\\hline\end{array}$$

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Definitions:

Causes Of Stress

Factors or situations that trigger a stress response, potentially affecting an individual's physical health, mental well-being, and overall quality of life.

Manage Stress

The process of identifying stressors and implementing strategies to cope with or reduce the impact of stress on one's life.

Work Day

A period during which work is carried out, typically conforming to the standard hours established by an employer or industry.

Resilience

The ability to recover quickly from difficulties; toughness and adaptability in the face of adversity.