Review Exercises 343 13. On a certain television channel, 18% of commercials are local advertisers. A sample of 120 commercials is selected. a. What is the probability that more than 20% of the commercials in the sample are local advertisers? 0.2843 Tech: 0.2842 b. Would it be unusual for more than 25% of the commercials to be local advertisers? Yes 14. Let X have a binomial distribution with n = 240 and p = 0.38. Use the normal approximation to find: a. P(X > 83) 0.8461 Tech: 0.8471 b. P(75 ≤ X ≤ 95) 0.7025 Tech: 0.7031 c. P(X < 96) 0.7157 Tech: 0.7163 15. Is it reasonable to treat the following sample as coming from an approximately normal population? Explain. Yes 5.5 8.7 9.3 10.1 15.2 3.5 11.9 7.6 13.7 8.7 14.3 5.8 Review Exercises 1. Find the area: Find the area under the standard normal curve a. To the left of z = 0.35 0.6368 b. To the right of z = −1.56 0.9406 c. Between z = 0.35 and z = 2.47 0.3564 2. Find the z-score: Find the z-score for which the area to its right is 0.89. −1.23 3. Your battery is dead: The lifetimes of a certain type of automobile battery are normally distributed with mean 5.9 years and standard deviation 0.4 year. The batteries are guaranteed to last at least 5 years. What proportion of the batteries fail to meet the guarantee? 0.0122 4. Take your medicine: Medication used to treat a certain condition is administered by syringe. The target dose in a particular application is 10 milligrams. Because of the variations in the syringe, in reading the scale, and in mixing the fluid suspension, the actual dose administered is normally distributed with mean �� = 10 milligrams and standard deviation �� = 1.6 milligrams. a. What is the probability that the dose administered is between 9 and 11.5 milligrams? 0.5621 Tech: 0.5598 b. Find the 98th percentile of the administered dose. 13.280 Tech: 13.286 c. If a clinical overdose is defined as a dose larger than 15 milligrams, what is the probability that a patient will receive an overdose? 0.0009 5. Lightbulbs: The lifetime of lightbulbs has a mean of 1500 hours and a standard deviation of 100 hours. A sample of 50 lightbulbs is tested. a. What is the probability that the sample mean lifetime is greater than 1520 hours? 0.0793 Tech: 0.0786 b. What is the probability that the sample mean lifetime is less than 1540 hours? 0.9977 c. What is the probability that the sample mean lifetime is between 1490 and 1550 hours? 0.7609 Tech: 0.7600 6. More lightbulbs: Someone claims to have developed a new lightbulb whose mean lifetime is 1800 hours with a standard deviation of 100 hours. A sample of 100 of these bulbs is tested. The sample mean lifetime is 1770 hours. a. If the claim is true, what is the probability of obtaining a sample mean that is less than or equal to 1770 hours? 0.0013 b. If the claim is true, would it be unusual to obtain a sample mean that is less than or equal to 1770 hours? Yes 7. Pay your taxes: Among all the state income tax forms filed in a particular state, the mean income tax paid was �� = $2000 and the standard deviation was �� = $500. As part of a study of the impact of a new tax law, a sample of 80 income tax returns is examined. Would it be unusual for the sample mean of these 80 returns to be greater than $2150? Yes 8. Safe delivery: A certain delivery truck can safely carry a load of 3400 pounds. The cartons that will be loaded onto the truck have a mean weight of 80 pounds with a standard deviation of 20 pounds. Forty cartons are loaded onto the truck. a. If the total weight of the 40 cartons is 3400 pounds, what is the sample mean weight? 85 pounds b. What is the probability that the truck can deliver the 40 cartons safely? 0.9429 Tech: 0.9431 9. Elementary school: In a certain elementary school, 52% of the students are girls. A sample of 65 students is drawn. a. What is the probability that more than 60% of them are girls? 0.0985 Tech: 0.0984 b. Would it be unusual for more than 70% of them to be girls? Yes 10. Facebook: Eighty percent of the students at a particular large university have logged on to Facebook at least once in the past week. A sample of 95 students is asked about their Internet habits. a. What is the probability that less than 75% of the sampled students have logged on to Facebook within the last week? 0.1112 Tech: 0.1115 b. What is the probability that more than 78% of the sampled students have logged on to Facebook within the last week? 0.6879 Tech: 0.6870 c. What is the probability that the proportion of the sampled students who have logged on to Facebook within the last week is between 0.82 and 0.85? 0.2009 Tech: 0.2015 11. It’s all politics: A politician in a close election race claims that 52% of the voters support him. A poll is taken in which 200 voters are sampled, and 44% of them support the politician.
navidi_monk_elementary_statistics_2e_ch7-9
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