Question 1: The amount of time until an accident occurs at an industrial facility follows an exponential distribution with mean 40 days. a) What is the probability that the next accident occurs between 50 and 100 days? b) What is the probability that the time until an accident occurs exceeds the mean time by more than 2 standard deviations? c) Suppose it has been at least 30 days with no accidents. What is the probability that it will be at least 80 days until an accident occurs?

Question 6 > 92% of the largest colleges and universities (more than 15,000 total enrollments) have some online offerings. Suppose you randomly pick 44 such intitutions, and let X be the number of intítutions that offer distance learning courses. a. What is the distribution of X? X - ? D Please show the following answers to 4 decimal places. b. What is the probability that exactly 37 intitutions in this study offer distance learning courses? c. What is the probability that at least 37 intitutions in this study offer distance learning courses? d. What is the probability that at most 37 intitutions in this study offer distance learning courses? e. What is the probability that between 35 and 42 (including 35 and 42) intitutions in this study offer distance learning courses? Check Answer

The lifetime (in years) of a specific helicopter part follows an exponential distribution whoseexpectation is 4 years.(a) What is the probability that one of these parts will stay operational for more than 4.4 years?(b) What is the probability that one of these parts will stay operational between 2.5 and 4 years.

The life of a certain type of device has an exponentially distributed failure with rate .008 per day. a) What is the mean time to failure? b) What is the probability that 200 days will pass before a failure is observed? c) What is the probability that 4 of the next 6 failures observed will occur after 200 days have passed? d) What is the probability that at most 3 failures will occur in 200 days?