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Chapter 6: Problem 44
In a standard Normal distribution, if the area to the left of a \(z\) -score is about \(0.1000\), what is the approximate \(z\) -score?
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A 2017 Pew Research Center report on drones found that only \(24 \%\) of Americans felt that drones should be allowed at events, like concerts or rallies. Suppose 100 Americans are randomly selected. a. What is the probability that exactly 25 believe drones should be allowed at these events? b. Find the probability that more than 30 believe drones should be allowed at these events. c. What is the probability that between 20 and 30 believe drones should be allowed at these events? d. Find the probability that at most 70 do not believe drones should be allowed at these events.
Quantitative SAT scores are approximately Normally distributed with a mean of 500 and a standard deviation of \(100 .\) On the horizontal axis of the graph, indicate the SAT scores that correspond with the provided \(z\) -scores. (See the labeling in Exercise 6.14.) Answer the questions using only your knowledge of the Empirical Rule and symmetry. a. Roughly what percentage of students earn quantitative SAT scores greater than \(500 ?\) i. almost all iii. \(50 \%\) \(\mathrm{v}\). about \(0 \%\) ii. \(75 \%\) iv. \(25 \%\) b. Roughly what percentage of students earn quantitative SAT scores between 400 and \(600 ?\) i. almost all iii. \(68 \%\) \(\mathrm{v}\). about \(0 \%\) ii. \(95 \%\) iv. \(34 \%\) c. Roughly what percentage of students earn quantitative SAT scores greater than \(800 ?\) i. almost all iii. \(68 \%\) \(\mathrm{v}\). about \(0 \%\) ii. \(95 \%\) iv. \(34 \%\) d. Roughly what percentage of students earn quantitative SAT scores les: than \(200 ?\) i. almost all iii. \(68 \%\) \(\mathrm{v}\). about \(0 \%\) ii. \(95 \%\) iv. \(34 \%\) e. Roughly what percentage of students earn quantitative SAT scores between 300 and \(700 ?\) i. almost all iii. \(68 \%\) v. \(2.5 \%\) ii. \(95 \%\) iv. \(34 \%\) f. Roughly what percentage of students earn quantitative SAT scores between 700 and 800 ? i. almost all iii. \(68 \%\) v. \(2.5 \%\) ii. \(95 \%\) iv. \(34 \%\)
According to the National Health Center, the heights of 6 -year-old girls are Normally distributed with a mean of 45 inches and a standard deviation of 2 inches. a. In which percentile is a 6 -year-old girl who is \(46.5\) inches tall? b. If a 6 -year-old girl who is \(46.5\) inches tall grows up to be a woman at the same percentile of height, what height will she be? Assume women are distributed as \(N(64,2.5)\).
Use the table or technology to find the answer to each question. Include an appropriately labeled sketch of the Normal curve for each part. Shade the appropriate region. A section of the Normal table is provided. a. Find the area in a Standard Normal curve to the left of \(1.13 .\) b. Find the area in a Standard Normal curve to the right of \(1.13 .\)
Survey data, the distribution of arm spans for males is approximately Normal with a mean of \(71.4\) inches and a standard deviation of \(3.3\) inches. a. What percentage of men have arm spans between 66 and 76 inches? b. Professional basketball player, Kevin Durant, has an arm span of almost 89 inches. Find the \(z\) -score for Durant's arm span. What percentage of males have an arm span at least as long as Durant's?
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