Probability Distributions

Let x represent the number of children in a household. The probability distribution of x is as follows: What is the expected value, E(x), of children in a randomly selected household? What is the probability that a randomly selected household will have more than 2 children?

4 wheel bearings are being put on a company vehicle. The mechanic is selecting the parts from a very large supply bin. 10% of the bearings in the bin are defective and will break within 100 miles. What is the probability the company vehicle will breakdown due to at least one wheel bearing failure tomorrow when it goes on its daily 111 mile delivery route?

Using the information from the last problem (n=4, p=.10), but instead of a very large parts bin, the mechanic selects the parts from a supply bin that contains only a total of 20. Now what’s the probability of breaking down?

According to a survey, 30% of the adult citizens of Shelbyville have a charge account at Susan’s Department Store. Susan’s brother is going to trial for embezzlement, and nine jurors are going to be selected at random. What’s the probability that at least four of the jurors will have a Susan’s charge account?

Over the lunch hour, cars arrive at the Credit Union ATM at the rate of 0.5 per minute. What is the probability that less than 5 cars will arrive at the ATM in the next 10 minutes.

Graduates from a large class at the state police academy score an average of 81.0 on their final exams. The scores are normally distributed with a standard deviation of 8.5 Graduates are randomly paired and assigned throughout the state. Bill scored 83.0 on his exam. What’s the probability that he will be paired with someone whose score was within 5.0 points of his?

A mail order store that sells running shoes has found that 20% of its orders are being returned for some problem. Each of the 100 members of the Tropic Lightning Running Club just order a pair of shoes from this company. The company manager promised the club a 15% discount on its next order if 10 or more of the pairs of shoes are returned. What is the probability of the club getting the 15% discount?

Homer, a circus performer, gets shot out of a cannon and lands in a net. The average distance he travels is 150 feet with a standard deviation of 30 feet. The net is 30 feet long. To maximize his chance of a safe landing, where should we put the front of the net? Would you be willing to substitute for Homer on his day off?

A high school play has five roles to fill with students. Sixteen students have expressed an interest in the play: 7 girls and 9 boys. What is the probability that exactly 3 girls will be selected?

A company sells toothpaste in a tube advertised to contain 8 ounces. The amount of toothpaste put in a tube is normally distributed with a mean of 8.21 ounces and a standard deviation of 0.09 ounces. If the actual capacity of the tubes used is 8.45 ounces, what is the probability that a randomly selected tube will be filled beyond capacity?

During the peak fishing months, a marina at a large reservoir noted that boats were arriving at the rate of 3.2 boats every twenty minutes to use the boat ramp. What is the probability that during the next twenty minutes the number of boats arriving to load or unload is exactly three?