Exam 5: Discrete Probability Distributions

An experiment consists of rolling a single die 12 times and the variable x is the number of times that the outcome is 6. Can the Poisson distribution be used to find the probability that the outcome of 6 occurs exactly 3 times, why or why not?

Describe the differences in the Poisson and the binomial distribution.

Sampling without replacement involves dependent events, so this would not be considered a binomial experiment. Explain the circumstances under which sampling without replacement could be considered independent and, thus, binomial.

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.

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.

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. Spinning a roulette wheel 9 times, keeping track of the occurrences of a winning number of "16)"

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?

Suppose that weight of adolescents is being studied by a health organization and that the accompanying tables describes the probability distribution for three randomly selected Adolescents, where x is the number who are considered morbidly obese. Is it significant to Have no obese subjects among three randomly selected adolescents? ( ) 0 0.111 1 0.215 2 0.450 3 0.224

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

Helene claimed that the expected value when rolling a fair die was 3.5. Steve said that wasn't possible. He said that the expected value was the most likely value in a single roll of the die, and since it wasn't possible for a die to turn up with a value of 3.5, the expected value couldn't possibly be 3.5. Who is right?

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).

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.

Assume that a procedure yields a binomial distribution with a trial repeated n = 30 times. Use the binomial probability formula to find the probability of x = 5 successes given the Probability p = 1/5 of success on a single trial. Round to three decimal places.

Use the given values of $n = 2112 , p = \frac { 3 } { 4 }$ 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.

For the table shown below, the random variable x is the number of males with tinnitu? (ringing ears)among four randomly selected males, based on a medical journal. Does the table describe a probability distribution? Why or why not? ( ) 0 0.674 1 0.280 2 0.044 3 0.003 4 0+

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?

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 a certain town, 22% of voters favor a given ballot measure. For groups of 21 voters, find the variance for the number who favor the measure.

The accompanying table shows the probability distribution for x, the number that shows up when a loaded die is rolled. ( ) 1 0.14 2 0.16 3 0.12 4 0.14 5 0.13 6 0.31

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