Exam 5: Discrete Probability Distributions

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

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 variance of the number of transactions per month for this subscriber?

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 probability that she gets audited once is ________.

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 produced between 5.0 and 8.0 inclusive bad bulbs.

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 produced at least 6.0 bad bulbs.

TABLE 5-2 A certain type of new business succeeds 60% of the time. Suppose that three such businesses open (where they do not compete with each other, so it is reasonable to believe that their relative successes would be independent). -Referring to Table 5-2, the probability that exactly one business succeeds is ________.

Suppose that the number of airplanes arriving at an airport per minute is a Poisson process. The average number of airplanes arriving per minute is 3. The probability that exactly 6 planes arrive in the next minute is 0.05041.

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 no more than one power outage 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 at least one retransmission is ________.

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 variance of the gain in value 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 fewer than two security transactions will be conducted in one month?

In a Poisson distribution, the mean and variance are equal.

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 fewer than six mishandled bags?

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 at least two 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 variance for the number of retransmissions 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 probability that she gets audited at least once is ________.

If the outcomes of a random variable follow a Poisson distribution, then their

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 neither sound an alarm in the presence of smoke is ________.

A company has 125 personal computers. The probability that any one of them will require repair on a given day is 0.025. To find the probability that exactly 20 of the computers will require repair on a given day, one will use what type of probability distribution?

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