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# 2 and z 16 soln p12z16 pz16 pz12 09452

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Unformatted text preview: ce P(X < x) = ? “z-score” how many SD’s z= x x−µ σ is above the mean P(X < x) = P(Z < z) Normal probabilities or proportions: steps 1.  State the problem in terms of x values and areas under a normal curve. 2.  Standardize: find the z scores using z=(x-mean)/SD and restate the problem in terms of these z values and corresponding areas under the standard normal curve. 3.  Use the empirical rule or software to find the required areas under the standard normal curve. v༇  NOTE: a)  b)  It is always useful to draw a picture showing the required areas. If you are using software, you can usually skip step 2. Finding Normal probabilities: Some example v༇  Find the area under the standard normal curve above 1. Soln: Using the empirical rule, P(Z>1) is approximately 16%, so 0.16 Using software[STATCRUNCH], P(Z>1) = 0.1587....
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