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Exam 5: Discrete Probability Distributions

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Question 31

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Match the following values as a A) discrete random variable, B) continuous random variable, or C) not a random variable: Exact weight of quarters now in circulation in the United States ______________ Shoe sizes of humans ____________________ Political party affiliations of adults in the United States _________________

A) B, A, C
B) C, A, B
C) A, B, C
D) A, C, B

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Question 32

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Reader's Digest ran a sweepstakes in which prizes were listed along with chances of winning: $1,000,000 (1 chance in 90,000,000), $100,000 (1 chance in 110,000,000), $25,000 (1 chance in 110,000,000), $5,000 (1 chance in 36,667,000), and $2,500 (1 chance in 27,500,000). Assuming that there is no cost of entering the sweepstakes, find the expected value of the amount won for one entry. If the cost of entering the sweepstakes is the cost of a postage stamp, is it worth entering the contest?

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The expected value is 1.2 cent...

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Question 33

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In a certain college, 33% of the physics majors belong to ethnic minorities. If 10 students are selected at random from the physics majors, what is the probability that no more than 6 belong to an ethnic minority? Round to three decimal places.

Mars, Inc. claims that 20% of its M&M plain candies are orange. A sample of 100 such candies is randomly selected. Find the mean and standard deviation for the number of orange candies in such groups of 100 .

List the three methods for finding binomial probabilities in the table below, and then complete the table to discuss the advantages and disadvantages of each. $\begin{array} { | l | l | l | } \hline \text { Methods } & \text { Advantage } & \text { Disadvantage } \\\hline & & \\\hline & & \\\hline & & \\\hline\end{array}$

A test consists of 10 true/false questions. To pass the test a student must answer at least 6 questions correctly. If a student guesses on each question, what is the probability that the student will pass the test? Round to three decimal places.

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. Rolling a single die 53 times, keeping track of the "fives" rolled.

In one town, the number of burglaries in a week has a Poisson distribution with a mean of 1.9 burglaries. Find the probability that in a randomly selected week the number of burglaries is at least three. Use the Poisson Distribution to find the indicated probability.

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 $\mu + 2 \sigma$

For the table shown below, the random variable x is the number of males with tinnitus (ringing ears)among four randomly selected males, based on a medical journal. Does the table describe a probability distribution? Why or why not? $\begin{array} { c | c } \boldsymbol { x } & \boldsymbol { P } ( \boldsymbol { x } ) \\\hline 0 & 0.674 \\1 & 0.280 \\2 & 0.044 \\3 & 0.003 \\4 & 0 +\end{array}$

Find the standard deviation, $\sigma$ , for the binomial distribution which has the stated values of n and p . Round your answer to the nearest hundredth. n=38 ; p=2 / 5

State the requirements to use the Poisson distribution as an approximation to the binomial distribution, including the mean for the Poisson distribution as an approximation to the binomial.

Based on a USA Today poll, assume that 10% of the population believes that college is no longer a good investment. Find the probability that among 16 randomly selected people, at least 1 believes that college is no longer a good investment.

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 braking time of a car. Identify the given random variable as being discrete or continuous

Multiple-choice questions on a test each have 5 possible answers, one of which is correct. Assume that you guess the answers to 5 such questions. a. Use the multiplication rule to find the probability that the first 2 guesses are wrong and the last 3 guesses are correct. That is, find P(WWCCC), where C denotes a correct answer and W denotes a wrong answer. b. Make a complete list of the different possible arrangements of 2 wrong answers and 3 correct answers, then find the probability for each entry in the list. c. Based on the preceding results, what is the probability of getting exactly 3 correct answers when 5 guesses are made?

Describe the Poisson distribution and give an example of a random variable with a Poisson distribution.

In a recent U.S. Open tennis tournament, among 20 of the calls challenged by the players, 8 were overturned after a review using an electronic system. Assume that when players challenge calls, they are successful in having them overturned 50% of the time. The probability that among 20 challenges, 8 or fewer are overturned is 0.252. Does this result suggest that the success rate is less than 50%? Why or why not?

Use the given values of n=93 and p=0.24 to find the minimum value that is not significantly low, $\mu - 2 \sigma$ , and the maximum value that is not significantly high, $\mu + 2 \sigma$ Round your answer to the nearest hundredth unless otherwise noted.

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: