1. The following table gives the probability distribution of a discrete random variable x.
x 0 1 2 3 4 5 6
P(x) .11 .19 .28 .15 .12 .09 .06
Find the following probabilities.
b) Probability that x assumes a value less than 4.
c) Probability that x assumes a value greater than 2.
2. A limousine has eight tires on it. A fleet of such limos was fit with a batch of tires that mistakenly passed quality testing. The following table lists the probability distribution of the number of defective tires on this fleet of limos where xx represents the number of defective tires on a limo and P(x) is the corresponding probability.
x 0 1 2 3 4 5 6 7 8
P(x) .0454 .1723 .2838 .2669 .1569 .0585 .0139 .0015 .0008
Calculate the mean and standard deviation of this probability distribution. Give a brief interpretation of the values of the mean and standard deviation.
3. Let xx be a discrete random variable that possesses a binomial distribution. Using the binomial formula, find the following probabilities.
a) p(5) for n=8 and p=.70
b) p(3) for n=4 and p=.40
Verify your answers by using Table I of Appendix B.
4. Let x be a discrete random variable that possesses a binomial distribution. If n = 5 and p = 0.8, then…
a) What is the mean (round to three decimal places)
b) What is the standard deviation of the probability distribution (round to three decimal places)?