1. Southpart Autos Offers a Variety of Luxury Options on Its Cars. Because of the 6 To

1. SouthPart Autos offers a variety of luxury options on its cars. Because of the 6 to 8 week waiting period for the customer orders, Ben Stolen, the dealer stocks his cars with a variety of options. Currently Mr stolen who prides himself on being able to meet his customers needs immediately, is worried because of an industry wise shortage of cars with V-8 engines. Stolen offers the following luxury combinations

1. V-8 engine, electric Sun roof, halogen headlights

2. Leather interiors, , power door locks, stereo cassette deck

3. Halogen headlights, V-8 Engine, Leather interior

4. Stereo cassette deck, V8 engine , power door locks

Stolen thinks that combination2,3 &4 have an equal chance of being ordered but the combination 1 is lower as likely to be ordered as any of these. What is the probability that any customer ordering a luxury car will order with V-8 engine?

2. A recent study of how Americans spend their leisure time surveyed workers employed more than 5 years. They determined the probability an employee has 2 weeks of vacation time to be .45, one week of vacation time to be .10 and 3 or more weeks to be .20. Suppose 20 workers are selected at random

a) What is the probablilty that only one worker has one week of vacation time?

b) What is the probability that atmost 2 workers have 3 or more weeks of vacation time?

3. Given the binomial distribution with n = 2.5 and p = .032, use the poisson approximation to the binomial to find. A) P[r=3] B)P[r<=1]

4. Median is a value x such that P[X=1/2. Mode of a distribution of X is a value x that maximizes f(x). If there is only one such x, it Is called the mode of the distribution

Find the median and of the pdf/p.m.f of X where

I. F(x)= (1/2)^x , x= 1,2,3,4…..

= 0 otherwise

II. f(x)= (½) (x^2 )(e^-x), 0

= 0 elsewhere

III. f(x) = 1/(b-a) if a

= 0 otherwise

5. Ashok tells the truth with probability 0.5 and kalpana with probability 0.4

I. If they make the same statement, what is the chance that the statement is true? II. If Ashok makes a statement and kalpana says that ashok lies, what is the probability that ashok told the truth?

(Hint: Use Bayes theorem)

6. Certain missile components are shipped in lots of 12. Three components are selected from each lot and a particular lot is accepted if one of the three components selected is defective. What is the probability that a lot will be accepted if it contains 5 defectives (Hint use hypergeometric distribution)