A car hire firm has cars which it hires out day by day. The number of demands for a car on each day is distributed as a poison fashion with mean 1.5. Calculate the probability on which (i) neither car is used (ii) more than 2 cars are in used

A car hire firm has cars which it hires out day by day. The number of demands for a car on each day is distributed as a poison fashion with mean 1.5. Calculate the probability on which (i) neither car is used (ii) more than 2 cars are in used

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Before every flight, the pilot must verify that the total weight of the load is less than the maximum allowable load for the aircraft. The aircraft can carry 42 passengers, and a flight has fuel and baggage that allows for a total passenger load of 7,056 lb. The pilot sees that the plane is full and all passengers are men. The aircraft will be overloaded if the mean weight of the passengers is greater than 7,056 lb42=168 lb. What is the probability that the aircraft is overloaded? Should the pilot take any action to correct for an overloaded aircraft? Assume that weights of men are normally distributed with a mean of 178.3 lb and a standard deviation of 36.8.
Dogsled drivers, known as mushers, use several different breeds of dogs to pull their sleds. One proponent of Siberian Huskies believes that sleds pulled by Siberian Huskies are faster than sleds pulled by other breeds. He times 4040 teams of Siberian Huskies on a particular short course, and they have a mean time of 7.77.7 minutes. The mean time on the same course for 4747 teams of other breeds of sled dogs is 6.26.2 minutes. Assume that the times on this course have a population standard deviation of 1.51.5 minutes for teams of Siberian Huskies and 1.61.6 minutes for teams of other breeds of sled dogs. Let Population 1 be sleds pulled by Siberian Huskies and let Population 2 be sleds pulled by other breeds. Step 1 of 2 : Construct a 95%95% confidence interval for the true difference between the mean times on this course for teams of Siberian Huskies and teams of other breeds of sled dogs. Round the endpoints of the interval to one decimal place, if necessary.
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