Confidence Interval (Possion Dist)

Suppose that 45 workers in a textile mill are selected at randome in a study of accident rate. the number of accidents per worker is assumed to be Poisson distributed with mean $\displaystyle \mu$. The average number of accidents per worker is $\displaystyle \overline{x}=1.7$.

a) Find an approximate one-sided lower 90% confidence limit for $\displaystyle \mu$ using CLT, that is, $\displaystyle (\overline{X}-\mu)/\sqrt{\mu/n}\rightarrow Z \sim N(0,1)$, where $\displaystyle X_i\sim POI(\mu)$

b) Repeat a) using $\displaystyle (\overline{X}-\mu)/\sqrt{\overline{X}/n}\rightarrow Z \sim N(0,1)$.

c)Find a conservative one-sided lower 90% confidence limit for $\displaystyle \mu$ .