Exam 5: Discrete Probability Distributions

A national trend predicts that women will account for half of all business travelers in the next 3 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 more than 7,but less than 13,of the hotels in the sample offered hairdryers in the bathrooms.

An Undergraduate Study Committee of 6 members at a major university is to be formed from a pool of faculty of 18 men and 6 women.If the committee members are chosen randomly,what is the probability that all of the members will be men?

TABLE 5-5 From an inventory of 48 new cars being shipped to local dealerships,corporate reports indicate that 12 have defective radios installed. -Referring to Table 5-5,what is the probability out of the 8 new cars it just received that,when each is tested,exactly two of the cars have non-defective radios?

Suppose that past history shows that 60% of college students prefer Brand C cola.A sample of 5 students is to be selected.The probability that exactly 1 prefers brand C 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 ________.

A lab orders 100 rats a week for each of the 52 weeks in the year for experiments that the lab conducts.Prices for 100 rats follow the following distribution: How much should the lab budget for next year's rat orders be,assuming this distribution does not change?

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

TABLE 5-11 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 5-11,what is the probability that no more than five security transactions will be conducted in one month?

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

If X has a binomial distribution with n = 4 and p = 0.3,then P(X > 1)= ________.

Which of the following about the binomial distribution is not a true statement?

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 3 power outages in a year is ________.

TABLE 5-7 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 5-7,if you can invest 30% of your money on the house in neighborhood A and the remaining on the house in neighborhood B,what is the portfolio risk of your investment?

If n = 10 and π = 0.70,then the standard deviation of the binomial distribution is

TABLE 5-4 The following table contains the probability distribution for X = the number of traffic accidents reported in a day in Corvallis,Oregon. -Referring to Table 5-4,the probability of at least 1 accident 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. -In a game called Taxation and Evasion,a player rolls a pair of dice.If on any turn the sum is 7,11,or 12,the player gets audited.Otherwise,she avoids taxes.Suppose a player takes 5 turns at rolling the dice.The expected number of times she will be audited is ________.

TABLE 5-9 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 5-9,what is the probability that in the next 1,000 customers,the hotel chain will have fewer than eight mishandled bags?

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 at least one retransmission is ________.

TABLE 5-8 Two different designs on a new line of winter jackets for the coming winter are available for your manufacturing plants.Your profit (in thousands of dollars)will depend on the taste of the consumers when winter arrives.The probability of the three possible different tastes of the consumers and the corresponding profits are presented in the following table. -Referring to Table 5-8,if you decide to choose Design A for 70% of the production lines and Design B for the remaining production lines,what is the expected profit?

TABLE 5-8 Two different designs on a new line of winter jackets for the coming winter are available for your manufacturing plants.Your profit (in thousands of dollars)will depend on the taste of the consumers when winter arrives.The probability of the three possible different tastes of the consumers and the corresponding profits are presented in the following table. -Referring to Table 5-8,if you decide to choose Design A for 10% of the production lines and Design B for the remaining production lines,what is the expected profit?