Exam 5: Discrete Probability Distributions

Suppose that a judge's decisions follow a binomial distribution and that his verdict is incorrect 10% of the time. In his next 10 decisions, the probability that he makes fewer than 2 incorrect verdicts is 0.736.

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

SCENARIO 5-3 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 Scenario 5-3, what is the standard deviation of the value gain for the house in neighborhood A?

SCENARIO 5-2 The following table contains the probability distribution for X = the number of traffic accidents reported in a day in a small city in the Midwest. X 0 1 2 3 4 5 P(X) 0.10 0.20 0.45 0.15 0.05 0.05 -Referring to Scenario 5-2, the probability of 3 accidents is ________.

SCENARIO 5-6 A certain type of new business succeeds 60% of the time. Suppose that 3 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 Scenario 5-6, the probability that all 3 businesses fail is ________.

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.

If π remains constant in a binomial distribution, an increase in n will increase the variance.

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?

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 ________.

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

SCENARIO 5-8 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 Scenario 5-8, what is the probability that any particular shift being inspected has produced at least 6.0 bad bulbs.

A probability distribution is an equation that

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

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.

SCENARIO 5-5 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 Scenario 5-5, the probability that neither sound an alarm in the presence of smoke is ________.

SCENARIO 5-7 A consulting firm that surveyed consumers' holiday shopping behavior found that the percentage of consumers from the U.S., Canada, and China who said that they planned to spend more on holiday shopping were 40%, 34% and 73%, respectively. The survey also found that the percentage of consumers from the U.S., Canada, and China who said that they were willing to share personal information with retailers in order to receive personalized offers from retailers were 55%, 46% and 72%, respectively. Suppose you randomly select 5 consumers from each of the three countries. -Referring to Scenario 5-7, the probability that at least 3 consumers from China are willing to share personal information with retailers in order to receive personalized offers from retailers is ________.

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

SCENARIO 5-7 A consulting firm that surveyed consumers' holiday shopping behavior found that the percentage of consumers from the U.S., Canada, and China who said that they planned to spend more on holiday shopping were 40%, 34% and 73%, respectively. The survey also found that the percentage of consumers from the U.S., Canada, and China who said that they were willing to share personal information with retailers in order to receive personalized offers from retailers were 55%, 46% and 72%, respectively. Suppose you randomly select 5 consumers from each of the three countries. -Referring to Scenario 5-7, the probability that all 5 consumers from China plan to spend more on holiday shopping 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 6.4 tickets per day. Find the probability that less than 6 tickets are written on a randomly selected day from this population.

The Department of Commerce in a particular state has determined that the number of small businesses that declare bankruptcy per month is approximately a Poisson distribution with a mean of 6.4. Find the probability that more than 3 bankruptcies occur next month.