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 \mu. The average number of accidents per worker is \overline{x}=1.7.

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