Exam 8: Probability Distributions and Statistics

The number of accidents that occur at a certain intersection known as "Five Corners" on a Friday afternoon between the hours of 3 P.M. and 6 P.M., along with the corresponding probabilities, are shown in the following table. Find the expected number of accidents during the period in question. Give your answer to three decimal places, if necessary. E = __________

The medical records of infants delivered at Kaiser Memorial Hospital show that the infants' lengths at birth (in inches) are normally distributed with a mean of 20 and a standard deviation of 2.6. Find the probability that an infant selected at random from among those delivered at the hospital measures more than 24 in. ​

Determine whether the given experiment is a binomial experiment. Justify your answer. ​ Casting a fair die 3 times and observing the number of times a 6 is thrown.

If the probability that a certain tennis player will serve an ace is , what is the probability that he will serve exactly two aces out of five serves? Round the answer to three decimal places, if necessary. The probability is __________.

Because of late cancellations, Neptune Lines, an operator of cruise ships, has a policy of accepting more reservations than there are accommodations available. From experience, 8% of the bookings for the 90-day around-the-world cruise on the S.S. Drion, which has accommodations for 2,000 passengers, are subsequently canceled. ​ If the management of Neptune Lines has decided, for public relations reasons, that a person who has made a reservation should have a probability of 0.97 of obtaining accommodation on the ship, determine the largest number of reservations that should be taken for a cruise on the S.S. Drion. ​ Round your answer to the nearest integer. ​ __________ reservations

The manager of C & R Clothiers, a major manufacturer of men's shirts, has determined that 3% of C & R's shirts do not meet with company standards and are sold as "seconds" to discount and outlet stores. What is the probability that in a day's production of 200 dozen shirts, less than 9 dozen will be classified as "seconds"?

Give the range of values that the random variable X may assume and classify the random variable as finite discrete, infinite discrete, or continuous. X = The number of times an accountant takes the CPA examination before passing

The histograms represent the probability distributions of the random variables X and Y. Determine by inspection which probability distribution has the larger variance. Answer a or b.

Find the variance of the probability distribution for the histogram. Give your answer to four decimal places, if necessary. Var (X) = __________

The probability distribution of a random variable X is Compute the mean, variance, and standard deviation of X.

A probability distribution has a mean of 46 and a standard deviation of 3. Use Chebychev's inequality to estimate the probability that an outcome of the experiment lies between 16 and 76. Give your answer to four decimal places, if necessary. At least __________ Use Chebychev's inequality to estimate the probability that an outcome of the experiment lies between 34 and 58. Give your answer to four decimal places, if necessary. At least __________

According to the data released by the Chamber of Commerce of a certain city, the weekly wages of factory workers are normally distributed with a mean of $650 and a standard deviation of $50. What is the probability that a worker selected at random from the city makes a weekly wage. Round your answers to four decimal places, if necessary.

Use the formula to determine the probability of the event. The probability of exactly two successes in eight trials of a binomial experiment in which . Round the answer to three decimal places, if necessary. The probability is __________.

Let X be the number of successes in 4 independent trials of a binomial experiment in which the probability of success is . Find and . ​ Round your answers to three decimal places, if necessary. ​ = __________ = __________

An advertisement for brand A chicken noodle soup claims that 50% of all consumers prefer brand A over other brands, the chief competitor's product. To test this claim, David Horowitz, host of The Consumer Advocate, selected eight people at random from the audience. After tasting both soups, each person was asked to state his or her preference. Assuming the company's claim is correct, find the probability that the company's claim was supported by the experiment; that is, four or more people stated a preference for brand A. Then find the probability the company's claim was not supported by the experiment; that is, fewer than four people stated a preference for brand A. Round your answers to three decimal places, if necessary. = __________ = __________

To be eligible for further consideration, applicants for certain Civil Service positions must first pass a written qualifying examination on which a score of 70 or more must be obtained. In a recent examination it was found that the scores were normally distributed with a mean of 67 points and a standard deviation of 6 points. Determine the percentage of applicants who passed the written qualifying examination. ​

The management of MultiVision, a cable TV company, intends to submit a bid for the cable television rights in one of two cities, A or B. If the company obtains the rights to city A, the probability of which is 0.4, the estimated profit over the next 10 years is $10 million; if the company obtains the rights to city B, the probability of which is 0.4, the estimated profit over the next 10 years is $8 million. The cost of submitting a bid for rights in city A is $200,000 and that of city B is $200,000. By comparing the expected profits for each venture, determine whether the company should bid for the rights in city A or city B. City __________

Let X denote the random variable that gives the sum of the faces that fall uppermost when two fair dice are cast. Find P(X = 7).

How many times must a person toss a coin if the chances of obtaining at least one head are 96% or better? __________ times

Find the value of the probability of the standard normal variable Z corresponding to the shaded area under the standard normal curve. Round your answer to four decimal places, if necessary. P ( Z < - 1.76 ) = __________