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October 25, 2006

Math 302 Assignment 6: Due Wednesday, November 1 at start of class

I. Problems to be handed in:

1. The number of times that an individual contracts a cold in a given year is a Poisson randomvariable with parameter = 5. Suppose a new wonder drug (based on large quantities of vitaminC) has just been marketed that reduces the Poisson parameter to = 3 for 75% of the population.For the other 25% of the population, the drug has no appreciable effect on colds. If an individualtries the drug for a year and has 2 colds in that time, how likely is it that the drug is beneficialfor him or her?

2. You arrive at a bus stop at 10:00, knowing that the bus will arrive at a time uniformly distributedbetween 10:00 and 10:30.

(a) What is the probability you will have to wait more than 10 minutes?

(b) If at 10:15 the bus has not yet arrived, what is the probability you will have to wait at leastan additional 10 minutes?

3. Lee figures that the total number of thousands of kilometers that an automobile can be drivenbefore it would need to be junked is an exponential random variable with parameter 1

40. Yang has

a used car that he claims has been driven only 20,000 kilometers.

(a) If Lee purchased the car, what is the probability that she would get at least 40,000 additionalkilometers out of it?

(b) Repeat under the assumption that the lifetime mileage of the car is not exponentially dis-tributed but rather is (in thousands of kilometers) uniformly distributed on (0, 80).

4. The width of a slot of a duralumin forging is (in cm) normally distributed with = .9000 and = .0030. The specification limits were given as .9000 .0050.

(a) What percentage of forgings will be defective?(b) What is the maximum allowable value of that will permit no more than 1 in 100 defectives

when the widths are normally distributed with = .9000 and ?

5. Suppose that the height, in cm, of a 25-year-old man is a normal random variable with parameters = 180, 2 = 40.3.

(a) What percentage of 25-year-old men are over 188 cm tall?

(b) What percentage of men over 183 cm tall are over 195 cm?

II. Recommended problems :

These problems from Scheaffer provide additional practice but are not to be handed in. Answers are

given in the text.#4.15, 4.16, 4.17, 4.20, 4.24,#4.31, 4.32, 4.33, 4.35, 4.37, 4.42,#4.55, 4.56, 4.57, 4.58, 4.59, 4.66.

Quote of the week: Math was always my bad subject. I couldnt convince my teachers that many of myanswers were meant ironically.

Calvin Trillin