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Unformatted text preview: Finding the Value of x Given a Proportion. • Draw a picture, with the area given shaded on it. • Look up the cumulative area in the middle of the z table, and look at the margins to find the z- score corresponding to that area. • Use the z-score formula to solve for x. Converting a z score to x: The relationship connecting x, z, μ and σ is. If you solve this equation for x you get x = μ + z σ IQ’s Revisited: The distribution of IQ scores is approximately normal with mean 100 and standard deviation 16. We can write this as X~N(100, 16). What IQ corresponds to: a) the bottom 20%? b) the top 5%? Jars of Sauce: A Company produces “20 ounce” jars of a sauce. The true amounts of sauce in the jars of this brand sauce follow a normal distribution. Suppose the companies “20 ounce” jars follow a N(20.2,0.125) distribution curve. (i.e., the contents of the jars are normally distributed with a true mean μ = 20.2 ounces with a true standard deviation and σ = 0.125 ounces. a. What proportion of the jars are under-filled (i.e., have less than 20 ounces of sauce)? ___________% of the jars contains less than 20 ounces of sauce. b. What proportion of the sauce jars contain between 20 and 20.3 ounces of sauce. _________% of the jars contain between 20 and 20.3 ounces of sauce. c. 99% of the jars of this brand of sauce will contain more than what amount of sauce? Time to Failure: The time to first failure of a unit of a brand of ink jet printer is approximately normally distributed with a mean of 1,500 hours and a standard deviation of 225 hours. a. What proportion of these printers will fail before 1,200 hours? b. What proportion of these printers will not fail within the first 2,000 hours? c. What should be the guarantee time for these printers if the manufacturer wants only 5% to fail within the guarantee period? d. What would the guaranteed period be? SAT Scores: SAT scores for each section are standardized so scores follow an approximately normal distribution with mean 500 points and standard deviation 100 points. We can write this as X~N(500, 100). The maximum score possible is 800 points....
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This note was uploaded on 04/21/2008 for the course MATH 220 taught by Professor Ruffin during the Fall '07 term at James Madison University.
- Fall '07