Exam 5: Discrete Probability Distributions

Find the indicated probability. -An archer is able to hit the bull's-eye 46% of the time. If she shoots 9 arrows, what is the probability that she gets exactly 4 bull's-eyes? Assume each shot is independent of the others.

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.

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?

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?

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. Methods Advantage Disadvantage

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 $\mu + 2 \sigma$ .

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. - $\mathrm { n } = 6 , \mathrm { x } = 3 , \mathrm { p } = \frac { 1 } { 6 }$

Provide an appropriate response. -If we sample from a small finite population without replacement, the binomial distribution should not be used because the events are not independent. If sampling is done without replacement and the outcomes belong to One of two types, we can use hypergeometric distribution. If a population has A objects of one type, while the Remaining B objects are of the other type, and if n objects are sampled without replacement, then the probability Of getting x objects of type A and (n - x) objects of type B is $P ( x ) = \frac { A ! } { ( A - x ) ! x ! } \cdot \frac { B ! } { ( B - n + x ) ! ( n - x ) ! } \div \frac { ( A + B ) ! } { ( A + B - n ) ! n ! }$ In a relatively easy lottery, a bettor selects 5 numbers from 1 to 13 (without repetition), and a winning 5-number Combination is later randomly selected. What is the probability of getting all 5 winning numbers? Round your Answer to four 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.

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.

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.

Answer the question. -Assume that there is a 0.05 probability that a sports playoff series will last four games, a 0.45 probability that it will last five games, a 0.45 probability that it will last six games, and a 0.05 probability that it will last seven Games. Is it unusual for a team to win a series in 7 games?

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. Round your answer to four decimal places.

() 1 0.037 2 0.200 3 0.444 4 0.296

Use the Poisson model to approximate the probability. Round your answer to four decimal places. -Suppose the probability of contracting a certain disease is p = 0.0006 for a new case in a given year. Use the Poisson distribution to approximate the probability that in a town of 6000 people there will be at least one new Case of the disease next year.

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. - $\mathrm { n } = 4 , \mathrm { x } = 3 , \mathrm { p } = \frac { 1 } { 6 }$

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. -Rolling a single "loaded" die 19 times, keeping track of the numbers that are rolled.

Solve the problem. -In a certain town, 20 percent of voters are in favor of a given ballot measure and 80 percent are opposed. For groups of 120 voters, find the mean for the number who oppose the measure.

Assume that a researcher randomly selects 14 newborn babies and counts the number of girls selected, x. The probabilities corresponding to the 14 possible values of x are summarized in the given table. Answer the question using the table. Probabilities of Girls x (girls) P(x) x (girls) P(x) x (girls) P(x) 0 0.000 5 0.122 10 0.061 1 0.001 6 0.183 11 0.022 2 0.006 7 0.210 12 0.006 3 0.022 8 0.183 13 0.001 4 0.061 9 0.122 14 0.000 -Find the probability of selecting exactly 8 girls.