statsII_study_sheet

statsII_study_sheet - Applications of the Normal Curve I....

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Applications of the Normal Curve I. Finding area/prob/percent A. z = x – mu/s to determine z. Round z to 2 dec. places. Look up area. 1. If problem says “higher than,” subtract area from 1. a. ex. SAT is normally distributed with mean of 1000 and standard deviation of 200. Find prob. That a student will score higher than 1300. i. identify values: mu = 1000, s = 200, x = 1300 ii. Solve z = x-mu/s. z = 1.50 iii. Look up area = .9332. 1-.9332 = .0668 2. If prob. Says “between,” solve z score twice. a. ex. Find prob. That student will score between 900 and 1200. i. identify values: mu = 1000, s = 200, x = 1200, 900 ii. Calculate 2 z scores: 1.00 and -0.50 iii. Look up areas and subtract: .8413-.3035=.5328 II. Finding x score given area B. x = mu + zs 1. ex. Applicants required to have SAT scores in 90 th percentile or higher to be eligible. What minimum score must be achieved to be eligible? a. Identify values: mu=1000, s=200, area = 90. b. Look up area and solve for x. 25=-0.67, x=866 3. Life span of machine is normally distributed w/ mean of 10.2 years and s of 1.7 years. Manufacturer willing to replace no more than 5% of machines. Find length of time manufacturer should set for guarantee. a. identify values: mu=10.2, s=1.7, area=.05 b. Look up area and solve for x. .05=-1.645. x=7.4 i. round values to match mean Conf. Int. for the mean The pop. Stand. Dev. Is known I. obtaining z score A. (100% - conf. lvl)/2. look up z score II. margin of error and conf. int. A. E = z(s/
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statsII_study_sheet - Applications of the Normal Curve I....

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