This requires the Poisson distribution, where area = 5-acres and mean number of field mice = 12 (in 5-acres of field) therefore lambda=12 (mean, given) and the probability of k mice in the 5-acre field is given by the Poisson distribution as P(X=k)=lambda^k * e^(-lambda) / k! ..............(1) To find the probability of having LESS than 7 field mice, we add the probabilities of 0 to 6, which is P(X<7)=P(X=0)+P(X=1)+...+P(X=6) evaluating with equation (1) for X=0 to 6, we get: 0 0.0000061 0.0000742 0.0004423 0.0017704 0.0053095 0.0127416 0.025481Total = 0.045822
Answer: The probability that fewer than 7 field mice are found in the 5-acre field is 0.0458.
