Exam 8: Probability Distributions

Among 10 videotapes that a retail store has available, four are comedies. If a customer selects three videotapes at random to buy for a friend, find the probability that: the following will occur. -None of them are comedies.

The binomial distribution Table $\mathrm{V}$ can be used to solve problems involving the binomial distribution if $\mathrm{n}$ has the values _______ and $p$ has the values _______.

The number of monthly breakdowns of a conveyor belt at a local factory is a random variable having the Poisson distribution with $\lambda=2.8$ . -Find the probability that the conveyor belt will function for a month without a breakdown. Round to the nearest thousandth.

If $2 \%$ of the checks received in an all night drugstore bounce, find the probability that in the next 100 checks received by the store, the following will occur. -Exactly 96 do not bounce.

A multiple choice test consists of seven questions with five choices each. If a student guesses on all questions the probability that a student gets exactly 3 correct answers is given by

A test has 12 multiple-choice questions with four answer choices for each question. Assume a student guesses on all questions.} -In the situation above, find the probability that she gets exactly five correct answers.

If $2 \%$ of the checks received in an all night drugstore bounce, find the probability that in the next 100 checks received by the store, the following will occur. -At most two bounce.

The probabilities of getting $0,1,2$ , or 3 heads in three flips of a balanced coin are, respectively, $\frac{1}{8}, \frac{3}{8}, \frac{3}{8}$ , and $\frac{1}{8}$ . Use the formulas that define $\mu$ and $\sigma^{2}$ to find the mean and the standard deviation of this probability distribution. If necessary, round to the nearest thousandth.

A test has 12 multiple-choice questions with four answer choices for each question. Assume a student guesses on all questions.} -In the situation above, find the mean.

According to the Mendelian theory of heredity, if plants with long violet petals are crossbred with plants with short white petals, the probabilities of getting a plant that has long violet petals, short violet petals, long white petals, or short white petals are, respectively, $\frac{9}{16}, \frac{3}{16}, \frac{3}{16}$ , and $\frac{1}{16}$ . What is the probability that among ten plants thus obtained there will be four with long violet petals, three with short violet petals, two with long white petals, and one with short white petals? If necessary, round to the nearest thousandth.

A test has 12 multiple-choice questions with four answer choices for each question. Assume a student guesses on all questions.} -In the situation above, find the probability that she gets at least three correct answers.

The probabilities that a customer entering a particular bookstore buys 0, 1, 2, 3, 4, or 5 books are 0.30, 0.20, 0.20, 0.15, 0.10, and 0.05 respectively. -For the probability distribution above, find the standard deviation.

In order to apply Chebyshev's theorem to determine the minimum fraction of data contained in a given interval, we need to know the _______ and the _______ of the distribution.

A test has 12 multiple-choice questions with four answer choices for each question. Assume a student guesses on all questions.} -In the situation above, find the standard deviation.

The probabilities that a customer entering a particular bookstore buys 0, 1, 2, 3, 4, or 5 books are 0.30, 0.20, 0.20, 0.15, 0.10, and 0.05 respectively. -For the probability distribution above, find the variance.

A study shows that $90 \%$ of the tomatoes shipped out by a large tomato grower are ripe and ready to eat. Find the probability that among 50 tomatoes shipped out by this grower all are ripe and ready to eat. Round to the nearest thousandth.

The daily number of people who examine cars in a particular automobile showroom is a random variable with $\mu=80$ and $\sigma=6$ . -Give the interval such that there is at least $35 / 36$ probability that the number of people who look at cars will be in that interval.

Experience has shown that $20 \%$ of a certain airline's flights leaving Green Field airport have to be delayed due to weather conditions. Determine the probability that among twenty flights at Green Field airport at most three will have to be delayed due to weather conditions. Round to the nearest thousandth.

In a problem involving the hypergeometric distribution, the binomial distribution may sometimes be used as an approximation.

Among 10 videotapes that a retail store has available, four are comedies. If a customer selects three videotapes at random to buy for a friend, find the probability that: the following will occur. -Two of them are comedies.