1. Normal Probability Distributions

2. Intro to Normal Distributions & the STANDARD Normal Distribution

3.  1. mean, median, and mode are equal  2. bell shaped and symmetric about the mean  3. total area under the curve is 1  4. the curve approaches, but never touches the x axis as it extends away from the mean

4.  A Normal distribution with  mean = 0 and  standard deviation = 1

5.  The cumulative area is close to 0 for z-scores close to z = -3.49  The cumulative area increases as the z-score increases.  The cumulative area for z = 0 is 0.5000  The cumulative area is close to 1 for z-scores close to z = 3.49

6. 1. Sketch the curve and shade the appropriate area under the curve. 2. To find the area LEFT of z, find the area that corresponds to z on the table. 3. To find the area RIGHT of z, find the area that corresponds to z on the table, then subtract from 1. 4. To find the area BETWEEN 2 z-scores, find each area, then subtract.

7.  1. left of z = -1.02  2. right of z = 2.30  3. left of z = 0.45  4. right of z = - 1.99  5. between z = -2.34 and z = 1.89

8. Normal Distributions: Finding Probabilities

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10. Find P(x < 200) Find P(x > 155) Find P(172 < x < 192)

11.  In a survey of US men, the heights in the 20 – 29 age group were normally distributed, with a mean of 69.4 inches and a standard deviation of 2.9 inches. Find the probability that a randomly selected participant has a height that is  A) less than 66 in.  B) between 66 and 72 in.  C) more than 72 in.  D) Identify any unusual events. Explain your reasoning.

12.  The amounts of time per workout an athlete uses a stairclimber are normally distributed, with a mean of 20 minutes and a standard deviation of 5 minutes. Find the probability that a randomly selected athlete uses a stairclimber for  A) less than 17 minutes.  B) between 20 and 28 minutes.  C) more than 30 minutes.

13.  SAT math scores are normally distributed with a mean of 514 and a standard deviation of 117.  A) What percent of the SAT math scores are less than 500?  B) Out of 1500 randomly selected SAT math scores, about how many would you expect to be greater than 600?