Name: Date: Pd: Review 8.3 & 8.4
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1 Name: Date: Pd: Review 8.3 & 8.4 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The histograms represent the probability distributions of the random variables X and Y. Determine by inspection which probability distribution has the larger variance. a. a b. b 2. Determine whether the given experiment is a binomial experiment. Justify your answer. Recording the number of accidents that occur at a given intersection on 4 clear days and 1 rainy day. a. Yes. The number of trials in the experiment is fixed. There are two outcomes of theexperiment. The probability of success in each trial is the same. The trials areindependent of each other. b. No the accidents depend of each other. c. No. The probability of an accident on a clear day is not the same as the probability ofan accident on a rainy day. Short Answer 3. A new drug has been found to be effective in treating 70% of the people afflicted by a certain disease. If the drug is administered to 600 people who have this disease, what is the standard deviation of the number of people for whom the drug can be expected to be effective?
2 4. The manager of a certain toy company has decided to accept a shipment of electronic games if there be no more than 1 defective electronic game in a random sample of 20. What is the probability that he will accept the shipment if 5% of the electronic games is defective? 5. The probability distribution of a random variable X is x P ( X = x ) Compute the mean, variance, and standard deviation of X. 6. The minimum age requirement for a regular driver's license differs from state to state. The frequency distribution for this age requirement in the 50 states is: Minimum Age Frequency of occurrence Compute the mean, variance, and standard deviation of the random variable X. 7. A probability distribution has a mean of 50 and a standard deviation of 1.5. Use Chebychev's inequality to find the value of c that guarantees that the probability is at least 93.75% that an outcome of the experiment lies between 50 - c and 50 + c.
3 8. A Christmas tree light has an expected life of 200 hr and a standard deviation of 2 hr. Suppose 110,000 of these Christmas tree lights are used by a large city as part of its Christmas decorations. Estimate the number of lights that will require replacement between 190 and 210 hr of use. 9. The McCormack Company manufactures solar panels. As a part of its quality control, the company checks the day s production by examining samples of 10. The following table shows the number of defective panels contained in a distribution of 55 samples. Number of Defective Panels in a Sample of 20 Number of Samples or more Find the mean number of defective panels per sample, and assuming that the distribution is binomial, estimate the percentage of defective solar panels in the day s production. (Round your final anwers upto two decimal places.) 10. An automobile manufacturing company uses fifteen industrial robots as welders on its assembly line. On a given working day, the probability that a robot will be inoperative is What is the probability that on a given working day exactly two robots are inoperative? More than two robots are inoperative? 11. If the probability that a certain tennis player will serve an ace is 0.2, what is the probability that he will serve at least two aces out of four serves?
4 12. The expected lifetime of the deluxe model hair dryer produced by Roland Electric has a mean life of 23 mo and a standard deviation of 2 mo. Find the probability that one of these hair dryers will last between 20 and 26 mo. 13. 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 six serves? 14. Find to four decimal places for the given values of n, x, and p. n = 5, x = 3, p = 0.7
5 Review 8.3 & 8.4 Answer Section MULTIPLE CHOICE 1. A 2. C SHORT ANSWER ,,. 6.,,. 7. c = , mean number of defective panels per sample = 0.89; percentage of defective solar panels in a day s production = 0.09% At least
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