Exam 5: Discrete Probability Distributions

TABLE 5-8 A major hotel chain keeps a record of the number of mishandled bags per 1,000 customers. In a recent year, the hotel chain had 4.06 mishandled bags per 1,000 customers. Assume that the number of mishandled bags has a Poisson distribution. -Referring to Table 5-8, what is the probability that in the next 1,000 customers, the hotel chain will have no more than two or at least eight mishandled bags?

If n = 10 and π = 0.70, then the mean of the binomial distribution is ________.

The number of power outages at a nuclear power plant has a Poisson distribution with a mean of 6 outages per year. The probability that there will be between 1 and 3 inclusive power outages in a year is ________.

TABLE 5-3 The following table contains the probability distribution for X = the number of retransmissions necessary to successfully transmit a 1024K data package through a double satellite media. -Referring to Table 5-3, the probability of no retransmissions is ________.

The Department of Commerce in a particular state has determined that the number of small businesses that declare bankruptcy per month is approximately a Poisson distribution with a mean of 6.4. Find the probability that more than 3 bankruptcies occur next month.

TABLE 5-6 There are two houses with almost identical characteristics available for investment in two different neighborhoods with drastically different demographic composition. The anticipated gain in value when the houses are sold in 10 years has the following probability distribution: -Referring to Table 5-6, what is the standard deviation of the value gain for the house in neighborhood A?

Thirty-six of the staff of 80 teachers at a local intermediate school are certified in cardio-pulmonary resuscitation (CPR). In 180 days of school, about how many days can we expect that the teacher on bus duty will likely be certified in CPR?

What type of probability distribution will most likely be used to analyze warranty repair needs on new cars in the following problem? The service manager for a new automobile dealership reviewed dealership records of the past 20 sales of new cars to determine the number of warranty repairs he will be called on to perform in the next 90 days. Corporate reports indicate that the probability any one of their new cars needs a warranty repair in the first 90 days is 0.05. The manager assumes that calls for warranty repair are independent of one another and is interested in predicting the number of warranty repairs he will be called on to perform in the next 90 days for this batch of 20 new cars sold.

Suppose that past history shows that 60% of college students prefer Coca-Cola. A sample of 10 students is to be selected. Which of the following distributions would you use to figure out the probability that at least half of them will prefer Coca-Cola?

TABLE 5-8 A major hotel chain keeps a record of the number of mishandled bags per 1,000 customers. In a recent year, the hotel chain had 4.06 mishandled bags per 1,000 customers. Assume that the number of mishandled bags has a Poisson distribution. -Referring to Table 5-8, what is the probability that in the next 1,000 customers, the hotel chain will have more than eight mishandled bags?

TABLE 5-5 The quality control manager of Green Bulbs Inc. is inspecting a batch of energy saving compact fluorescent light bulbs. When the production process is in control, the mean number of bad bulbs per shift is 6.0. -Referring to Table 5-5, what is the probability that any particular shift being inspected has less than 5.0 or more than 8.0 bad bulbs.

The diameters of 10 randomly selected bolts have a binomial distribution.

TABLE 5-8 A major hotel chain keeps a record of the number of mishandled bags per 1,000 customers. In a recent year, the hotel chain had 4.06 mishandled bags per 1,000 customers. Assume that the number of mishandled bags has a Poisson distribution. -Referring to Table 5-8, what is the probability that in the next 1,000 customers, the hotel chain will have more than five but less than eight mishandled bags?

A national trend predicts that women will account for half of all business travelers in the next three years. To attract these women business travelers, hotels are providing more amenities that women particularly like. A recent survey of American hotels found that 70% offer hairdryers in the bathrooms. Consider a random and independent sample of 20 hotels. Find the probability that at least 9 of the hotels in the sample do NOT offer hairdryers in the bathrooms.

The number of 911 calls in Butte, Montana, has a Poisson distribution with a mean of 10 calls a day. The probability of two or more 911 calls in a day is ________.

The connotation "expected value" or "expected gain" from playing roulette at a casino means

The number of power outages at a nuclear power plant has a Poisson distribution with a mean of 6 outages per year. The probability that there will be at least one power outage in a year is ________.

A national trend predicts that women will account for half of all business travelers in the next three years. To attract these women business travelers, hotels are providing more amenities that women particularly like. A recent survey of American hotels found that 70% offer hairdryers in the bathrooms. Consider a random and independent sample of 20 hotels. Find the probability all of the hotels in the sample offered hairdryers in the bathrooms.

TABLE 5-9 Subscribers to Investment Advice White Letters perform security transactions at the rate of five trades per month. Assume that one of the subscribers performs transactions at this rate and the probability of a transaction for any two months is the same and the number of transactions in one month is independent of the number of transactions in another month. -Referring to Table 5-9, what is the mean number of transactions per month for this subscriber?

If π remains constant in a binomial distribution, an increase in n will increase the variance.