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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
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:
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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- Fall '07
- Normal Distribution, standard normal curve