1. For a binomial distribution, n=number of trials, p=probability of success and q=probability of failure. For which one of the following situations would the Normal Distribution approximation not be considered an adequate estimation?
2. If a key witness is called, the probability that a ceratin suspect will be found guilty is .90. Historically, the probability that a key witness is called whenever a suspect is found guilty is .75. If the probability that this key witness is called to testify is .65, what is the probabilty that this suspect will be found guilty?
3. Using the Poisson distribution function, if 1.2 accidents can be expected at a certain intersection every day, what is approximately the probability that there will be two accidents at that intersection on any given day?
4. Given a probability distribution in which the randon varible X assumes only the values 0,1,2,3,4, suppose P(X=2) = .08, P(X=3) = .12, and P(X=4) = .22, which of the following must be true?
5. Which one of the following binomial experiments contains two trials per outcome?
6. Let P(X) = X/48 represent a probability function. If the random variable X assumes only 4 consecutive odd numbers, what is the largest value of P(X)?
7. Assume that the tires sold by Olsen Tires are normally distributed with a mean life of 43,000 miles and a standard deviation of 2,000 miles. If you were to buy 4 Olsen tires, what is the approximate probability that all four will last longer than 42,000 miles?
8. What if you buy 6 Olsen tires; approximately what is the probability that they will average less than 41,500 miles?
9. Which two of the following are probability distributions? I. P(X) = X2 for X= .3, .4, .5 II. P(X) = X/3, for X=1, 2 III. P(X) = X - 1.5 for X=2,3 IV. P(X) = 3/(5*(X+1)!), for X=0,1,2
I. P(X) = X2 for X= .3, .4, .5 II. P(X) = X/3, for X=1, 2 III. P(X) = X - 1.5 for X=2,3 IV. P(X) = 3/(5*(X+1)!), for X=0,1,2
10. Given events A and B, where P(not A) = .25, P(A union B)= .875 and the P(A intersection B) = .2, what is the P(B)?