STATISTICS ELEMENTARY MARIO F. TRIOLA EIGHTH EDITION Section 5-3 Normal Distributions: Finding Probabilities MARIO F. TRIOLA EIGHTH EDITION

Other Normal Distributions If   0 or  1 (or both), we could convert values to standard scores (z scores) using the formula: Then we could use the procedures for working with the standard normal distribution. But . . . we can also use the TI-83 directly by specifying the mean and standard deviation as follows: normalcdf(lower, upper, mean, sd) page 241 of text

Probability of Weight between 143 pounds and 201 pounds There is a 0.4772 probability of randomly selecting a woman with a weight between 143 and 201 lbs. OR: 47.72% of women have weights between 143 lb and 201 lb. μ = 143 σ =29 page 242 of text Weight 143 201 Figure 5-14

STATISTICS ELEMENTARY MARIO F. TRIOLA Section 5-4 Normal Distributions: Finding Values MARIO F. TRIOLA EIGHTH EDITION

Cautions to keep in mind 1. Don’t confuse z scores and areas.     Z scores are distances along the horizontal  scale, but areas are regions under the  normal curve. page 249 of text

Finding z Scores when Given Probabilities 95% 5% 1.645 FIGURE 5-11 Finding the 95th Percentile

Finding z Scores when Given Probabilities 90% 10% Student will need to be reminded that Table A-2 will not indicate that the correct z score for this problem will be negative. This is something that the student will have to remember to do when writing the correct answer to the problem. Emphasize the number line aspect again and that numbers below 0 will be negative. -1.28 FIGURE 5-12 Finding the 10th Percentile

Finding a value when given a probability using the TI-83 Draw a normal curve, draw the centerline, shade the region under the curve that corresponds to the given probability, and enter the probability value in the region. If the area shaded is not to the left of the desired value desired, subtract the probability from 1 to find the area to the left of the desired value. Press [2nd] [DISTR], select 3:invNorm(, type area, mean, sd and press enter. page 249-250 of text

Finding P10 for Weights of Women 10% 90% μ = 143 σ =29 Drawing for example on page 250 of text Weight x = 106 143 The weight of 106 lb (rounded) separates the lowest 10% from the highest 90%. FIGURE 5-17