Troy University Probability and Statistics Problem

The Marine Expeditionary Unit (MEU) assigned to the JTF has 12 CH-46 helicopters. Each can carry 25 passengers.According to current (1980) OSD data, each has an availability of 74%. That means that on any given day, there is a 74% chance that the aircraft is mission capable.The time between helicopter failures requiring a mission abort is estimated to be 25 flying hours. These failure times follow an exponential distribution. We expect that 100 passengers will need to be flown out by helicopter. Passenger weight is normally distributed with a mean of 185 pounds and a standard deviation of 30 pounds.

(8 points) Determine and graph the distribution of the number of available helicopters.
(8 points) Find the mean number of available helicopters.
(8 points) Find the approximate 5th percentile of helicopters available on any given day. What does this number mean in the context of this mission?
(8 points) Each helicopter has a planned mission length of 2.5 hours. Find the probability that a helicopter fails requiring a mission abort in this time period. Does it matter how many hours it has been since the last breakdown?
(8 points) The number of non-combatants to be rescued in a given sortie is estimated at 100. How many helicopters should be sent to be 95% sure that enough complete the mission?
(8 points) You plan on 25 passengers per helicopter. Find and graph the distribution of total passenger weight per helicopter. Find the 95th percentile of total passenger weight.
(8 points) In your professional opinion, do you have sufficient helicopters for this mission requirement? Why or why not?

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