Exam 5: Discrete Probability Distributions

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.

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. -Multiple-choice questions on a test each have 4 possible answers, one of which is correct. Assume that you guess the answers to 4 such questions. a. Use the multiplication rule to find the probability that the first two guesses are wrong and the third and fourth guesses are correct. That is, find P(WWCC), 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 2 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 2 correct answers when 4 guesses are made?

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

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. - $\mathrm { n } = 30 , \mathrm { x } = 12 , \mathrm { p } = 0.20$

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 399 jawbreakers that weigh more than .4 ounces?

Reader's Digest ran a sweepstakes in which prizes were listed along with chances of winning: $1,000,000 (1chance in 90,000,000), $100,000 (1 chance in 110,000,000), $25,000 (1 chance in 110,000,000), $5000 (1 chance in 36,667,000), and $2500 (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?

() 0 0.26 1 0.11 2 0.16 3 0.05 4 0.42

Find the indicated probability. -A tennis player makes a successful first serve 51% of the time. If she serves 9 times, what is the probability that she gets exactly 3 first serves in? Assume that each serve is independent of the others.

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 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 4 girls.

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. - $n = 5 , x = 2 , p = 0.70$

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 12 or more girls.

Find the indicated probability. Round to three decimal places. -An airline estimates that 94% of people booked on their flights actually show up. If the airline books 73 people on a flight for which the maximum number is 71, what is the probability that the number of people who show Up will exceed the capacity of the plane?

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. - $\mathrm { n } = 48 ; \mathrm { p } = 3 / 5$

Find the indicated probability. Round to three decimal places. -The participants in a television quiz show are picked from a large pool of applicants with approximately equal numbers of men and women. Among the last 11 participants there have been only 2 women. If participants are Picked randomly, what is the probability of getting 2 or fewer women when 11 people are picked?

Find the mean, µ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth. - $\mathrm { n } = 38 ; \mathrm { p } = 0.2$

Find the mean, µ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth. - $\mathrm { n } = 1665 ; \mathrm { p } = 0.57$

Based on a Comcast survey, there is a 0.8 probability that a randomly selected adult will watch prime-time TV live, instead of online, on DVR, etc. Assume that seven adults are randomly selected. Find the probability that Fewer than three of the selected adults watch prime-time live.

If a person is randomly selected from a certain town, the probability distribution for the number, x, of siblings is as described in the accompanying table. () 0 0.25 1 0.32 2 0.22 3 0.10 4 0.05 5 0.04

Provide an appropriate response. -In a game, you have a $1 / 36$ probability of winning $85 and a 35/36 probability of losing $4. What is your expected value?