ST_370_Exam_2_Study_Guide_2

ST_370_Exam_2_Study_Guide_2 - a. However, in our course,...

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a. However, in our course, you do not need to interpolate, but rather choose one of the two values. In this case since the two closest tabulated probabilities, 0.9495 and 0.9505, were equidistant from 0.95, we just took the average of the row/column values 1.64 and 1.65 to get 1.645. You would get credit in this course for using 1.64 or 1.65 or 1.645. Typical General Normal Probability Problems: Let X be a N (10, 25) random variable (r.v.), where the mean μ is 10 and the variance σ 2 is 25, and the standard deviation (s.d.) is 5. Find the following probabilities. a. Find Pr( X < 0.2). First, we need to transform the general normal r.v. to the standard normal r.v. Z by using Z = ( X -μ)/σ. After making this transformation, the problem becomes Pr( X < 0.2) = Pr(( X - 10)/5 < (0.2 - 10)/5) = Pr( Z < -1.96) = 0.025. b. Find Pr( X < 19.8). The transformation given in (a) leads to Pr( Z < (19.8 - 10)/5) = Pr( Z <1.96) = 0.975. c. Pr(3.6 < X < 19.8) = Pr((3.6 - 10)/5 < Z < (19.8-10)/5) = Pr(-1.28 < Z < 1.96) = Pr( Z < 1.96) - Pr( Z < -1.28) = 0.975 - Pr( Z > 1.28) = 0.975 - (1 -.8997) = 0.8747. d. Pr(| X - 10| < 8.225) = Pr(|( X - 10)/5| < 8.225/5) = Pr(| Z | < 1.645) = Pr (-1.645 < Z < 1.645) = 0.90. Typical General Normal Percentile Problems:
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ST_370_Exam_2_Study_Guide_2 - a. However, in our course,...

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