An industrial plant has an average of 1.5 accidents occurring every three months and it is assumed that this same rate applies to any time interval of interest (e.g., if one was interested in a one-month period the appropriate rate would be 0.5 accidents per month). In the last three months, four accidents have occurred.

a. What distribution describes the random variable x? Explain.

b. Calculate the probability of no accidents occurring during the current three-month period.

c. Find the probability that fewer accidents will occur during the current three-month period than during the last three months.

d. Calculate the probability of no more than 12 accidents occurring in a given year.

e. Find the probability of no accidents occurring for a particular year.