Exam 5: Discrete Probability Distributions

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. - $\mathrm { n } = 42 ; \mathrm { p } = 3 / 5$

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

Identify each of the variables in the Binomial Probability Formula. $P ( x ) = \frac { n ! } { ( n - x ) ! x ! } \cdot p ^ { x } \cdot q ^ { n - x }$ Also, explain what the fraction $\frac { n ! } { ( n - x ) ! x ! }$ computes.

A company manufactures calculators in batches of 55 and claims that the rate of defects is 4%. Find the probability of getting exactly 2 defects in a batch of 55 if the rate of defects is 4%. If a store receives a batch of 55 calculators and finds that there are 2 defective calculators, do they have any reason to doubt the company's claimed rate of defects?

In a certain town, 30% of voters favor a given ballot measure. For groups of 34 voters, find the variance for the number who favor the measure.

The probability that a radish seed will germinate is 0.7. A gardener plants seeds in batches of 14. Find the mean for the number of seeds germinating in each batch.

The probability is 0.2 that a person shopping at a certain store will spend less than $20. For groups of size 11, find the mean number who spend less than $20.

Identify the given random variable as being discrete or continuous. -The braking time of a car

Use the given values of n and p to find the minimum usual value $\mu - 2 \sigma \text { and the maximum usual value } \mu + 2 \sigma$ . Round your answer to the nearest hundredth unless otherwise noted. - $\mathrm { n } = 103 , \mathrm { p } = 0.26$

Suppose a mathematician computed the expected value of winnings for a person playing each of seven different games in a casino. What would you expect to be true for all expected values for these seven games?

Find the mean, $\mu$ , for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth. - $\mathrm { n } = 37 ; \mathrm { p } = 0.2$

A 28-year-old man pays $118 for a one-year life insurance policy with coverage of $140,000. If the probability that he will live through the year is 0.9993, what is the expected value for the insurance Policy?

Find the standard deviation, ?, for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. - $\mathrm { n } = 41 ; \mathrm { p } = 0.2$

Determine whether the following is a probability distribution. If not, identify the requirement that is not satisfied. -A police department reports that the probabilities that 0, 1, 2, 3, and 4 car thefts will be reported in a given day are 0.223, 0.335, 0.251, 0.126, and 0.047, respectively.

Find the indicated probability. Round to three decimal places. -A company purchases shipments of machine components and uses this acceptance sampling plan: Randomly select and test 26 components and accept the whole batch if there are fewer than 3 defectives. If a particular shipment of thousands of components actually has a 6% rate of defects, What is the probability that this whole shipment will be accepted?

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 ( girls ) () ( girls ) () ( girls ) () 0 0.000 5 0.122 10 0.061 1 0.001 6 0.183 11 0.022 2 0.006 7 0.209 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 9 or more girls.

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 whether the given procedure results in a binomial distribution. If not, state the reason why. -Rolling a single "loaded" die 11 times, keeping track of the numbers that are rolled.

Multiple-choice questions on a test each have 6 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?

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 10 participants there have been only 2 women. If participants are picked randomly, what is the probability of getting 2 or fewer women when 10 people are picked?