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Chapter 6: Problem 9
For the standard normal distribution, what does \(z\) represent?
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According to the College Board (http://professionals.collegeboard.com/gateway), the mean SAT mathematics score for all college-bound seniors was 511 in 2011 . Suppose that this is true for the current population of college-bound seniors. Furthermore, assume that \(17 \%\) of college-bound seniors scored below 410 in this test. Assume that the distribution of SAT mathematics scores for college-bound seniors is approximately normal. a. Find the standard deviation of the mathematics SAT scores for college-bound seniors. b. Find the percentage of college-bound seniors whose mathematics SAT scores were above 660 .
Major League Baseball rules require that the balls used in baseball games must have circumferences between 9 and \(9.25\) inches. Suppose the balls produced by the factory that supplies balls to Major League Baseball have circumferences normally distributed with a mean of \(9.125\) inches and a standard deviation of \(.06\) inch. What percentage of these baseballs fail to meet the circumference requirement?
Alpha Corporation is considering two suppliers to secure the large amounts of steel rods that it uses. Company A produces rods with a mean diameter of \(8 \mathrm{~mm}\) and a standard deviation of \(.15 \mathrm{~mm}\) and sells 10,000 rods for \(\$ 400\). Company B produces rods with a mean diameter of \(8 \mathrm{~mm}\) and a standard deviation of \(.12 \mathrm{~mm}\) and sells 10,000 rods for \(\$ 460\). A rod is usable only if its diameter is between \(7.8 \mathrm{~mm}\) and \(8.2 \mathrm{~mm}\). Assume that the diameters of the rods produced by each company have a normal distribution. Which of the two companies should Alpha Corporation use as a supplier? Justify your answer with appropriate calculations.
The pucks used by the National Hockey League for ice hockey must weigh between \(5.5\) and \(6.0\) ounces. Suppose the weights of pucks produced at a factory are normally distributed with a mean of \(5.75\) ounces and a standard deviation of \(.11\) ounce. What percentage of the pucks produced at this factory cannot be used by the National Hockey League?
Find the value of \(z\) so that the area under the standard normal curve a. from 0 to \(z\) is \(.4772\) and \(z\) is positive b. between 0 and \(z\) is (approximately) \(.4785\) and \(z\) is negative c. in the left tail is (approximately) . 3565 d. in the right tail is (approximately) \(.1530\)
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