One of the earliest applications of the Poisson distribution was made by Student (1907)...

One of the earliest applications of the Poisson distribution was made by Student (1907) in studying errors made in counting yeast cells or blood corpuscles with a haemacytometer. In this study, yeast cells were killed and mixed with water and gelatin; the mixture was then spread on a glass and allowed to cool. Four different concentrations were used. Counts were made on 400 squares, and the data are summarized in the following table:

a. Estimate the parameter λ for each of the four sets of data.

b. Find an approximate 95% confidence interval for each estimate.

c. Compare observed and expected counts.