An author showed that the number of soldiers in a country's cavalry killed due to a certain type of accident in each of 14 cavalry corps over a 20-year period followed a Poisson distribution. The data summary follows.

Number of deaths	Frequency
0	141
1	89
2	29
3	13
4	2

(a)Find the mean number of deaths per year per cavalry unit. [HINT:

Use the formula for the mean of grouped data.] (Round your answer to two decimal places.)

(b)Use the result of part

(a) and the Poisson distribution to find the probability of exactly one death per unit per year. (Round your answer to three decimal places.)

(c)Find the probability of at most two deaths per year. (Round your answer to three decimal places.)

(d)How do the probabilities in parts

(b) and

(c) compare to the observed relative frequencies in the table?

(Round your answers to three decimal places.)From the table, the proportion of times that one soldier was killed is .

The probability calculated from the Possion probability is .

Based on the table the proportion of times that at most two soldiers were killed is . Based on the Poisson distribution at most two soldiers were killed is .