Exam 5: Some Important Discrete Probability Distributions

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

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 2 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 ________.

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, what is the standard deviation of your profit when Design A is chosen?

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

The Poisson distribution can be used to model a continuous random variable.

TABLE 5-6 The quality control manager of Green Bulbs Inc. is inspecting a batch of energy saving fluorescent light bulbs. When the production process is in control, the average number of bad bulbs per shift is 6.0. -Referring to Table 5-6, what is the probability that any particular shift being inspected has produced between 5.0 and 8.0 inclusive bad bulbs?

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?

The expected return of a two-asset portfolio is equal to the product of the weight assigned to the first asset and the expected return of the first asset plus the product of the weight assigned to the second asset and the expected return of the second asset.

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 5-8 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 90% of the production lines and Design B for the remaining production lines, what is the coefficient of variation of your investment?

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?

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 at least 1 prefers brand C 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, what is the expected value gain for the house in neighborhood B?

TABLE 5-9 A major hotel chain keeps a record of the number of mishandled bags per 1,000 customers. In 2009, 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 six mishandled bags?

The number of power outages at a nuclear power plant has a Poisson distribution with a mean of 6 outages per year. The variance of the number of power outages is ________.

The local police department must write, on average, 5 tickets a day to keep department revenues at budgeted levels. Suppose the number of tickets written per day follows a Poisson distribution with a mean of 6.5 tickets per day. Interpret the value of the mean.

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, what is the expected profit if you increase the shift of your production lines and choose to produce both designs?

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 ________.

The number of males selected in a sample of 5 students taken without replacement from a class of 9 females and 18 males has a binomial distribution.

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?