GetFood (a food delivery company) wants to investigate the customers ordering behavior on its' mobile app on a weekday lunchtime. The server administrator collects a sample of 400 inter-arrival times (in seconds) of food ordering requests from the mobile app to its server during lunchtime. The mean inter-arrival times is 0.1563 seconds.

a) Calculate the mean food order request arrival rate () to its server.

Use the exponential distribution model as appropriate to answer questions b) to c)

b)Calculate the probability that the inter-arrival time from one food order request to the next is less than 0.1s.

c)Calculate the probability that the inter-arrival time from one food order request to the next is between 0.1s and 0.3s.

Use the Poisson distribution model as appropriate to answer questions d) and e)

d)Calculate the probability that three food order requests will arrive to the server in a particular interval of one second.

e)Calculate the probability that three or more food order requests will arrive to the server in a particular interval of one second.

f)Using the t-statistic, construct a 95% confidence interval for the mean inter-arrival time of food order request to the server.