Exam 5: Some Important Discrete Probability Distributions

The number of 911 calls in Butte, Montana, has a Poisson distribution with a mean of 10 calls a day. The probability of 2 or more 911 calls in a day 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: Price: \ 10.00 \ 12.50 \ 15.00 Probability: 0.35 0.40 0.25 How much should the lab budget for next year's rat orders be, assuming this distribution does not change?

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 most 2 prefer brand C is_____

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____ .

When using a Poisson distribution to approximate a binomial distribution, the standard deviation of the Poisson distribution is np where n is the sample size and p is the probability of an event of interest.

TABLE 5-4 The following table contains the probability distribution for X = the number of traffic accidents reported in a day in Corvallis, Oregon. 0 1 2 3 4 5 P() 0.10 0.20 0.45 0.15 0.05 0.05 -Referring to Table 5-4, the mean or expected value of the number of accidents is____ .

$\text { TABLE 5-7 }$ 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: $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Returns }$ Prob ability Neighb or hood A Neighb or hood B .25 -\ 22,500 \ 30,500 .40 \ 10,000 \ 25,000 .35 \ 40,500 \ 10,500 -Referring to Table 5-7, what is the variance of the gain in value for the house in neighborhood A?

$\text { TABLE 5-4 }$ The following table contains the probability distribution for X = the number of traffic accidents reported in a day in Corvallis, Oregon. 0 1 2 3 4 5 P() 0.10 0.20 0.45 0.15 0.05 0.05 -Referring to Table 5-4, the probability of 3 accidents 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. Probability Taste Design A Design B 0.2 more conservative 180 520 0.5 no change 230 310 0.3 more liberal 350 270 -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 expected profit?

A lab orders 100 rats a week for each of the 52 weeks in the year for experiments that the lab conducts. Suppose the mean cost of rats used in lab experiments turned out to be $13.00 per week. Interpret this value.

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 _____.

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

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

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 4 prefer brand C is_____

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

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 _____.

$\text { TABLE 5-7 }$ 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: $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Returns }$ Prob ability Neighb or hood A Neighb or hood B .25 -\ 22,500 \ 30,500 .40 \ 10,000 \ 25,000 .35 \ 40,500 \ 10,500 -Referring to Table 5-7, what is the expected value gain if you invest in both houses?

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 all of the hotels in the sample offered hairdryers in the bathrooms.

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 1 power outage in a year is ____.

$\text { TABLE 5-3 }$ 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. X 0 1 2 3 P(X) 0.35 0.35 0.25 0.05 -Referring to Table 5-3, the probability of no retransmissions is _____.