Exam 5: Discrete Probability Distributions

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 5 girls.

Do probability distributions measure what did happen or what will probably happen? How do we use probability distributions to make decisions?

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. - $\mathrm { n } = 29 ; \mathrm { p } = 0.2$

Determine whether the following is a probability distribution. If not, identify the requirement that is not satisfied. x P(x) 0 0.1296 1 0.3456 2 0.3456 3 0.1536 4 0.0256

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.

() 0 0.29 1 0.21 2 0.09 3 0.36 4 0.05

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

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. $n = 38 ; p = 2 / 5$

Use the Poisson model to approximate the probability. Round your answer to four decimal places. -The probability that a car will have a flat tire while driving through a certain tunnel is 0.00004. Use the Poisson distribution to approximate the probability that among 11,000 cars passing through this tunnel, at most two will Have a flat tire.

Find the indicated probability. -A company manufactures calculators in batches of 55 and claims that the rate of defects is 5%. Find the probability of getting exactly 3 defects in a batch of 55 if the rate of defects is 5%. If a store receives a batch of 55 Calculators and finds that there are 3 defective calculators, do they have any reason to doubt the company's Claimed rate of defects?

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. -Spinning a roulette wheel 7 times, keeping track of the winning numbers.

The following table describes the results of roadworthiness tests of Ford Focus cars that are three years old (based on data from the Department of Transportation). The random variable x represents the number of cars That failed among six that were tested for roadworthiness: x P(x) 0 0.377 1 0.399 2 0.176 3 0.041 4 0.005 5 0+ 6 0+ Find the probability of getting three or more cars that fail among six cars tested.

Use the Poisson model to approximate the probability. Round your answer to four decimal places. -The probability that a car will have a flat tire while driving through a certain tunnel is 0.00004. Use the Poisson distribution to approximate the probability that among 7000 cars passing through this tunnel, at least one will Have a flat tire.

On a multiple choice test with 17 questions, each question has four possible answers, one of which is correct. For students who guess at all answers, find the mean for the number of correct answers.

Solve the problem. -The probability that a person has immunity to a particular disease is 0.2. Find the mean number who have immunity in samples of size 30.

Find the indicated probability. -The brand name of a certain chain of coffee shops has a 46% recognition rate in the town of Coffleton. An executive from the company wants to verify the recognition rate as the company is interested in opening a Coffee shop in the town. He selects a random sample of 8 Coffleton residents. Find the probability that exactly 4 Of the 8 Coffleton residents recognize the brand name.

Provide an appropriate response. Round to the nearest hundredth. -In a certain town, 70% of adults have a college degree. The accompanying table describes the probability distribution for the number of adults (among 4 randomly selected adults) who have a college degree. Find the Standard deviation for the probability distribution. () 0 0.0081 1 0.0756 2 0.2646 3 0.4116 4 0.2401

Answer the question. -Suppose that voting in municipal elections is being studied and that the accompanying tables describes the probability distribution for four randomly selected people, where x is the number that voted in the last election. Is it unusual to find four voters among four randomly selected people?

Answer the question. -Suppose that a law enforcement group studying traffic violations determines that the accompanying table describes the probability distribution for five randomly selected people, where x is the number that have Received a speeding ticket in the last 2 years. Is it unusual to find no speeders among five randomly selected People? () 0 0.08 1 0.18 2 0.25 3 0.22 4 0.19 5 0.08