Exam 5: Discrete Probability Distributions

Identify the given random variable as being discrete or continuous. The cost of a randomly selected orange.

Find the indicated mean. -A classical example of the Poisson distribution involves the number of deaths caused by horse kicks to men in the Prussian Army between 1875 and 1894. Data for 9 corps were combined for the 20-year period, and the 180 Corps-years included a total of 135 deaths. Suppose the Poisson distribution will be used to find the probability That a randomly selected corps-year has more than 2 deaths. Find the mean of the appropriate Poisson Distribution (the mean number of deaths per corps-year). Round your answer to the nearest hundredth.

A police department reports that the probabilities that 0, 1, 2, and 3 burglaries will be reported in a given day are 0.54, 0.43, 0.02, and 0.01, respectively.

In a Gallup poll of randomly selected adults, 66% said that they worry about identity theft. For a group of 1013 adults, the mean of those who do not worry about identify theft is closest to ________.

Provide an appropriate response. Round to the nearest hundredth. -The random variable x is the number of houses sold by a realtor in a single month at the Sendsom's Real Estate Office. Its probability distribution is as follows. Find the standard deviation for the probability distribution. Houses Sold () Probability () 0 0.24 1 0.01 2 0.12 3 0.16 4 0.01 5 0.14 6 0.11 7 0.21

A die is rolled nine times and the number of times that two shows on the upper face is counted. If this experiment is repeated many times, find the mean for the number of twos.

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. -Rolling a single die 26 times, keeping track of the numbers that are rolled.

The number of golf balls ordered by customers of a pro shop has the following probability distribution. () 3 0.14 6 0.29 9 0.36 12 0.11 15 0.10

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. -n =12, x = 5, p = 0.25

Use the Poisson model to approximate the probability. Round your answer to four decimal places. -The probability that a car will have a flat tire while driving through a certain tunnel is 0.00005. Use the Poisson distribution to approximate the probability that among 14,000 cars passing through this tunnel, exactly two will Have a flat tire.

Answer the question. -Assume that there is a 0.15 probability that a basketball playoff series will last four games, a 0.30 probability that it will last five games, a 0.25 probability that it will last six games, and a 0.30 probability that it will last Seven games. Is it unusual for a team to win a series in 7 games?

Use the Poisson Distribution to find the indicated probability. -The number of calls received by a car towing service averages 19.2 per day (per 24-hour period). After finding the mean number of calls per hour, find the probability that in a randomly selected hour the number of calls is 2)

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. -Choosing 5 marbles from a box of 40 marbles (20 purple, 12 red, and 8 green) one at a time with replacement, keeping track of the colors of the marbles chosen.

A company manufactures batteries in batches of 6 and there is a 3% rate of defects. Find the mean number of defects per batch.

A certain rare form of cancer occurs in 37 children in a million, so its probability is 0.000037. In the city of Normalville there are 74,090 children. A Poisson distribution will be used to approximate the probability that The number of cases of the disease in Normalville children is more than 2. Find the mean of the appropriate Poisson distribution (the mean number of cases in groups of 74,090 children).

The number of oil spills occurring off the Alaskan coast

A survey for brand recognition is done and it is determined that 68% of consumers have heard of Dull Computer Company. A survey of 800 randomly selected consumers is to be conducted. For such groups of 800, Would it be significant to get 634 consumers who recognize the Dull Computer Company name? Consider as Significant any result that differs from the mean by more than 2 standard deviations. That is, significant values Are either less than $\mu - 2 \sigma$ or greater than $\mu + 2 \sigma$

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. -n = 7, x = 4 , p = 0.5

Determine if the outcome is unusual. Consider as unusual any result that differs from the mean by more than 2 standard deviations. That is, unusual values are either less than $\mu - 2 \sigma$ or greater than $\mu + 2 \sigma$ -The Acme Candy Company claims that 8% of the jawbreakers it produces actually result in a broken jaw. Suppose 9571 persons are selected at random from those who have eaten a jawbreaker produced at Acme Candy Company. Would it be unusual for this sample of 9571 to contain 801 persons with broken jaws?

The Acme Candy Company claims that $60 \%$ of the jawbreakers it produces weigh more than $0.4$ ounces. Suppose that 800 jawbreakers are selected at random from the production lines. Would it be significant for this sample of 800 to contain 494 jawbreakers that weigh more than $0.4$ ounces? Consider as significant any result that differs from the mean by more than 2 standard deviations. That is, significant values are either less than $\mu$ $2 \sigma$ or greater than $\mu + 2 \sigma$ .