Exam 5: Discrete Probability Distributions

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

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 standard deviation of the number of times she will be audited 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 standard deviation of the number of accidents is ________.

TABLE 5-7 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 5-7, what is the standard deviation of your profit when Design B is chosen?

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 expected value gain for the house in neighborhood B?

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 probability that at least five security transactions will be conducted in one month?

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 ten mishandled bags?

In a binomial distribution,

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 probability that more than two security transactions will be conducted in one month?

Another name for the mean of a probability distribution is its expected value.

TABLE 5-7 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 5-7, what is the standard deviation of your profit when Design A is chosen?

A multiple-choice test has 30 questions. There are 4 choices for each question. A student who has not studied for the test decides to answer all questions randomly. What type of probability distribution can be used to figure out his chance of getting at least 20 questions right?

A professor receives, on average, 24.7 e-mails from students the day before the midterm exam. To compute the probability of receiving at least 10 e-mails on such a day, he will use what type of probability distribution?

TABLE 5-1 The probability that a particular type of smoke alarm will function properly and sound an alarm in the presence of smoke is 0.8. You have two such alarms in your home and they operate independently. -Referring to Table 5-1, the probability that both sound an alarm in the presence of smoke is ________.

The on-line access computer service industry is growing at an extraordinary rate. Current estimates suggest that 75% of the home-based computers have access to on-line services. Suppose 20 people with home-based computers were randomly and independently sampled. Find the probability that more than 9 of those sampled currently do NOT have access to on-line services.

If π remains constant in a binomial distribution, an increase in n will not change the mean.

Whenever π = 0.5, the binomial distribution will

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 variance of the number of accidents is ________.

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 mean or expected value of the number of accidents is ________.