1. 16.1 Approximate Normal Approximately Normal Distribution: Almost a bell shape curve. Normal Distribution: Bell shape curve. All perfect bell shape curves are normal curves. Discrete Math

2. 16.2 Normal Distribution: center = median (M) = mean (  ) Approx Normal: Median  Mean. Point of inflection: transition point of being bent upward to downward. Normal Distribution: The standard Deviation equals the distance between a point of inflection and the axis of symmetry. Discrete Math To be continued…

3. 16.2 (Continued...) Q 1   - (0.675)  Q 3   + (0.675)  Discrete Math

4. 16.3 Standardizing Normal Data Measuring data values using the standard deviation. Standardizing Original Data x Standardized Data z = (x-  ) /  (z-value) Discrete Math

5. 16.4 68 - 95 - 99.7 Rule 68% of data within one standard deviation from the mean. 95% of data within two standard deviations from the mean. 99.7% of data within three standard deviations from the mean. Range  6  Discrete Math

6. 16.5 - 7 Honest coin principal: A coin is tossed n times and X is the number of heads. The random variable X has an approximately normal distribution with mean  = n / 2 and standard deviation  =  n / 2 256 tosses:  = 256 / 2 = 128,  =  256 / 2 = 8 Discrete Math To be continued…

7. 16.5 - 7 (Continued...) Dishonest coin principal: A dishonest coin is tossed n times and X is the number of heads. Suppose p is the probability of heads and (1-p) is the probability of tails. The random variable of X has an approximately normal distribution with mean  = n * p and standard deviation  =  ( n * p * (1 - p)) 1000 light bulbs, 20% defects:  = 1000(.20) = 200  =  1000 * (.20) * (1 -.20) Discrete Math To be continued…

8. 16.5 - 7 (Continued...) Standard Error: The standard deviation of the sampling distribution expressed as a percentage.  / N Confidence Intervals: 95% two standard deviations from the mean. 99.7 three standard deviations from the mean. Discrete Math