Question

10. The length of time for one individual to be served at a cafeteria is a random variable having an exponential distribution with a mean of 4 minutes. (a) What is the probability that a person is served in less than 3 minutes? (b) What is the probability that a person is served in less than 3 minutes on at least 4 of the next 6 days? (Hint: use binomial distribution.)

Answer 1

here for exponential distribution paramter $\beta$ =4

a) probability that a person is served in less than 3 minutes =P(X<3) =1-e^-x/$\beta$ =1-e^-3/4 =0.5276

b)

here for binomial distirbution p=0.5276 and n=6

hence probability of at least 4 of next 6 days ; person will be served in 3days

=$\sum_{x=4}^{6}\binom{6}{x}(0.5276)^{x}(1-0.5276)^{6-x}$ =0.3969