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M ARIO F . T RIOLA

S TATISTICS. E LEMENTARY. Section 5-3 Normal Distributions: Finding Probabilities. M ARIO F . T RIOLA. E IGHTH. E DITION. Other Normal Distributions. If   0 or   1 (or both), we could convert values to standard scores ( z scores) using the formula:

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M ARIO F . T RIOLA

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

  2. Other Normal Distributions If  0or 1 (or both), we couldconvert 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)

  3. 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 Weight 143201 Figure 5-14

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

  5. 1. Don’t confuse zscores and areas. Z scores are distances along the horizontal  scale, but areas are regions under the  normal curve. 2. Don’t confuse probabilities with data values. Given values, find probabilities: use normalcdf. Given probabilities, find values: use invnorm. Cautions to keep in mind

  6. Finding z Scores when Given Probabilities 95% 5% 1.645 0 FIGURE 5-11 Finding the 95th Percentile

  7. Finding z Scores when Given Probabilities 90% 10% -1.28 0 FIGURE 5-12 Finding the 10th Percentile

  8. Finding a value when given a probabilityusing 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.

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

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