Step-by-step explanation:
a. #We notice this is a Poisson probability function expressed as:
x-number of occurrences in a given interval.
-mean occurrences of the event
-The mean is calculated as:
#the probability of no accidents in a 15-minute period is :
Hence, the probability of no accident in a 15-min period is
b. The the probability of at least one accident in a 15-minute period. is calculated as:
Hence, the probability of at least one accident in a 15-minute period is
c. The probability of four or more accidents in a 15-minute period is calculated as:
Hence,the probability of four or more accidents in a 15-minute period. is 0.9997