Exam 5: Discrete Probability Distributions

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 $\mu + 2 \sigma$ -According to AccuData Media Research, 36% of televisions within the Chicago city limits are tuned to "Eyewitness News" at 5:00 pm on Sunday nights. At 5:00 pm on a given Sunday, 2500 such televisions are Randomly selected and checked to determine what is being watched. Would it be unusual to find that 981 of the 2500 televisions are tuned to "Eyewitness News"?

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. -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?

Solve the problem. -The probability that a radish seed will germinate is 0.7. A gardener plants seeds in batches of 15. Find the standard deviation for the number of seeds germinating in each batch.

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 .

Find the mean, µ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth. - $\mathrm { n } = 676 ; \mathrm { p } = 0.7$

Use the Poisson Distribution to find the indicated probability. -The number of lightning strikes in a year at the top of a particular mountain has a Poisson distribution with a mean of 3.8. Find the probability that in a randomly selected year, the number of lightning strikes is 0.

Solve the problem. -On a multiple choice test with 9 questions, each question has four possible answers, one of which is correct. For students who guess at all answers, find the variance for the number of correct answers.

In a magazine survey, 427 women are randomly selected without replacement and each woman is asked what she purchases online. Responses consist of whether clothing was identified. Determine whether the given procedure results in a distribution that is either binomial or can be treated as binomial. If not binomial, identify at least one requirement that is not satisfied.

Solve the problem. -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.

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?

Find the indicated mean. -An insurance company in the town of Codrington sells life insurance. They are determining the premium for a $100,000 life insurance for a 50-year old woman. The probability that a 50-year old woman in Codrington Survives the year is 0.9963. The company sells 1200 such policies to 50-year old females. The company will use The Poisson distribution to approximate the probability of various number of deaths during the year in this Group of 1200 women. Find the mean of the appropriate Poisson distribution (the mean number of deaths in a Year in such groups of 1200 females). Round your answer to the nearest hundredth.

Find the mean, µ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth. - $\mathrm { n } = 38 ; \mathrm { p } = 3 / 5$

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 $\mu + 2 \sigma$ -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 unusual to get 494 consumers who recognize the Dull Computer Company name?

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. - $\mathrm { n } = 38 ; \mathrm { p } = 0.4$

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 60% of the jawbreakers it produces weigh more than .4 ounces. Suppose that 800 jawbreakers are selected at random from the production lines. Would it be unusual for this sample of 800 to contain 494 jawbreakers that weigh more than .4 ounces?

According to a college survey, 22% of all students work full time. Find the mean for the number of students who work full time in samples of size 16.

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

The number of freshmen in the required course, English 101

Solve the problem. -The probability of winning a certain lottery is $\frac { 1 } { 72,639 }$ . For people who play 664 times, find the standard deviation for the number of wins.

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.