Exam 5: Discrete Probability Distributions

If you are conducting an experiment where the probability of a success is .02 and you are interested in the probability of 4 successes in 15 trials, the correct probability function to use is the

General Hospital has noted that they admit an average of 8 patients per hour. a.Define the random variable in words for this experiment. b.What is the probability that during the next hour fewer then 3 patients will be admitted? c.What is the probability that during the next two hours exactly 8 patients will be admitted?

The standard deviation of a binomial distribution is

June's Specialty Shop sells designer original dresses. On 10% of her dresses, June makes a profit of $10, on 20% of her dresses she makes a profit of $20, on 30% of her dresses she makes a profit of $30, and on 40% of her dresses she makes a profit of $40. On a given day, the probability of June having no customers is .05, of one customer is .10, of two customers is .20, of three customers is .35, of four customers is .20, and of five customers is .10. a. What is the expected profit June earns on the sale of a dress? b. June's daily operating cost is $40 per day. Find the expected net profit June earns per day. (Hint: To find the expected daily gross profit, multiply the expected profit per dress by the expected number of customers per day.) c. June is considering moving to a larger store. She estimates that doing so will double the expected number of customers. If the larger store will increase her operating costs to $100 per day, should she make the move?

The number of customers at Winkies Donuts between 8:00a.m. and 9:00a.m. is believed to follow a Poisson distribution with a mean of 2 customers per minute. a. During a randomly selected one-minute interval during this time period, what is the probability of 6 customers arriving to Winkies? b. What is the probability that at least 2 minutes elapse between customer arrivals?

An experiment consists of making 80 telephone calls in order to sell a particular insurance policy. The random variable in this experiment is the number of sales made. This random variable is a

Ten percent of the items produced by a machine are defective. Out of 15 items chosen at random, a.what is the probability that exactly 3 items will be defective? b.what is the probability that less than 3 items will be defective? c.what is the probability that exactly 11 items will be non-defective?

Telephone calls arrive at the Global Airline reservation office in Louisville according to a Poisson distribution with a mean of 1.2 calls per minute. a. What is the probability of receiving exactly one call during a one-minute interval? b. What is the probability of receiving at most 2 calls during a one-minute interval? c. What is the probability of receiving at least two calls during a one-minute interval? d. What is the probability of receiving exactly 4 calls during a five-minute interval? e. What is the probability that at most 2 minutes elapse between one call and the next?

Waters' Edge is a clothing retailer that promotes its products via catalog and accepts customer orders by all of the conventional ways including the Internet. The company has gained a competitive advantage by collecting data about its operations and the customer each time an order is processed. Among the data collected with each order are: number of items ordered, total shipping weight of the order, whether or not all items ordered were available in inventory, time taken to process the order, customer's number of prior orders in the last 12 months, and method of payment. For each of the six aforementioned variables, identify which of the variables are discrete and which are continuous.

An insurance company has determined that each week an average of nine claims are filed in their Atlanta branch. What is the probability that during the next week a.exactly seven claims will be filed? b.no claims will be filed? c.less than four claims will be filed? d.at least eighteen claims will be filed?

Exhibit 5-6 Probability Distribution -Refer to Exhibit 5-6. The expected value of x equals

Excel's BINOM.DIST function can be used to compute

The expected value of a discrete random variable

Before dawn Josh hurriedly packed some clothes for a job-interview trip while his roommate was still sleeping. He reached in his disorganized sock drawer where there were five black socks and five navy blue socks, although they appeared to be the same color in the dimly lighted room. Josh grabbed six socks, hoping that at least two, and preferably four, of them were black to match the gray suit he had packed. With no time to spare, he then raced to the airport to catch his plane. a. What is the probability that Josh packed at least two black socks so that he will be dressed appropriately the day of his interview? b. What is the probability that Josh packed at least four black socks so that he will be dressed appropriately the latter day of his trip as well?

Exhibit 5-8 The student body of a large university consists of 60% female students. A random sample of 8 students is selected. -Refer to Exhibit 5-8. What is the probability that among the students in the sample exactly two are female?

Exhibit 5-11 The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3. -Refer to Exhibit 5-11. The expected value of the random variable x is

Exhibit 5-4 A local bottling company has determined the number of machine breakdowns per month and their respective probabilities as shown below. -Refer to Exhibit 5-4. The probability of no breakdowns in a month is

In the textile industry, a manufacturer is interested in the number of blemishes or flaws occurring in each 100 feet of material. The probability distribution that has the greatest chance of applying to this situation is the

Excel's HYPGEOM.DIST function can be used to compute

Shoppers enter Hamilton Place Mall at an average of 120 per hour. a.Define the random variable in words for this experiment. b.What is the probability that exactly 5 shoppers will enter the mall between noon and 1:00 p.m.? c.What is the probability that exactly 5 shoppers will enter the mall between noon and 12:05 p.m.? d.What is the probability that at least 35 shoppers will enter the mall between 5:00 and 5:10 p.m.?