Exam 8: Probability Distributions and Statistics

Use the appropriate normal distribution to approximate the resulting binomial distribution. ​ Bearings is the principal supplier of ball bearings for the Sperry Gyroscope Company. It has been determined that 6% of the ball bearings shipped are rejected because they fail to meet tolerance requirements. What is the probability that a shipment of 200 ball bearings contains more than 14 rejects? ​ Round your answer to four decimal places, if necessary. ​ The probability is __________.

Make a sketch of the area under the standard normal curve corresponding to the given probability. P ( Z < 1.35 )

The following table gives the scores of 30 students in a mathematics examination. Find the mean and the standard deviation of the distribution of the given data. Round the answers to the nearest hundredth, if necessary. Hint: Assume that all scores lying within a group interval take the midvalue of that group. __________ __________

Use the appropriate normal distribution to approximate the resulting binomial distribution. Colorado Mining and Mineral has 800 employees engaged in its mining operations. It has been estimated that the probability of a worker meeting with an accident during a 1-year period is .1. What is the probability that more than 80 workers will meet with an accident during the 1-year period?

Let X be the number of successes in 4 independent trials of a binomial experiment in which the probability of success is . Find . ​

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. ​ Round your answer to the nearest hundredth, if necessary. ​ __________%

The odds against an event E occurring are 1 to 7. What is the probability of E not occurring? Give your answer to three decimal places, if necessary. The probability is __________.

Suppose a probability distribution of a random variable X is represented by the accompanying histogram. Shade that part of the histogram whose area gives the probability .

The speeds (in mph) of motor vehicles on a certain stretch of Route 3A as clocked at a certain place along the highway are normally distributed with a mean of 61.2 mph and a standard deviation of 8.44 mph. ​ Round your answers to four decimal places, if necessary. ​ What is the probability that a motor vehicle selected at random is traveling at more than 62 mph? ​ __________ ​ What is the probability that a motor vehicle selected at random is traveling at less than 57 mph? ​ __________ ​ What is the probability that a motor vehicle selected at random is traveling at between 62 and 69 mph? ​ __________

The probability distribution of a random variable X is Compute the mean, variance, and standard deviation of X. Round your answers to the nearest hundredth, if necessary. __________ Var (X) = __________ __________

An experiment consists of casting an eight-sided die (numbered 1 through 8) and observing the number that appears uppermost. Find the mean and variance of this experiment.

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. ​

The speeds (in mph) of motor vehicles on a certain stretch of Route 3A as clocked at a certain place along the highway are normally distributed with a mean of 68.2 mph and a standard deviation of 8.44 mph. What is the probability that a motor vehicle selected at random is traveling at between 72 and 74 mph?

The following table gives the 2002 age distribution of U.S. population: Let the random variable X denote a randomly chosen age group within the population. What percentage of the U.S. population is between 20 to 44 years old, inclusive?

Find the value of the probability of the standard normal variable Z corresponding to this area. P ( 0.49 < Z < 1.74 )

Use the appropriate normal distribution to approximate the resulting binomial distribution. ​ Preview Showcase, a research firm, screens pilots of new TV shows before a randomly selected audience and then solicits their opinions of the shows. Based on past experience, 20% of those who get complimentary tickets are "no-shows." The theater has a seating capacity of 500. Management has decided, for public relations reasons, that a person who has been solicited for a screening should have a probability of .99 of being seated. ​ How many tickets should the company send out to prospective viewers for each screening? ​ __________ tickets

The management of the Cambridge Company has projected the sales of its products (in millions of dollars) for the upcoming year, with the associated probabilities shown in the following table: What does the management expect the sales to be next year?

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

Find the value of the probability of the standard normal variable Z corresponding to the shaded area under the standard normal curve.

An examination consisting of ten true-or-false questions was taken by a class of 100 students. The probability distribution of the random variable X, where X denotes the number of questions answered correctly by a randomly chosen student, is represented by the accompanying histogram. The rectangle with base centered on the number 8 is missing. What should be the height of this rectangle? ​ ​