Question 3a. An expensive machine has had 14 failures in the past 1095 days. (More than one failure can occur on a single day, although this is unlikely.)

If the failure rate is a constant that must be estimated from data, what is a 95% upper confidence limit for the failure rate (average failures per day), based on the above data?

Question 3b.Suppose that the failure rate is known to be exactly 0.014 failures per day.What is the probability that the machine will operate for the next 30 days with no failures?

(Answer up to 4 decimal places)

Answer in R