2 Properties of Normal Distribution PeakImage text page 487It’s peak occurs directly above the meanThe curve is symmetric about the vertical line through the mean.The curve never touches the x-axisThe area under the curve is always = 1. (This agrees with the fact that the sum of the probabilities in any distribution is 1.)
3 Variations in Normal Curves One standard deviation is smaller than normalOne standard deviation is equal to the normalOne standard deviation is larger than normal
4 The Area Under the Standard Normal Curve 1 standard deviationABImage from text p 487The area of the shaded region under a normal curve form a point A to B is the probability that an observed data value will be between A and BBetween -1 and +1 standard deviations there is 68% of the region, therefore the probability of an observed data value being within 1 standard deviation is 68%, etc.
5 Problem solved using the Standard Normal Curve The area under a normal curve to the left of x (the data) is the same as the area under the standard normal curve to the left of the z-score for x.What does that mean?The z-score is the formula that converts the raw data (x) from a normal distribution into the lookup values of a STANDARD NORMAL CURVE. [See table in appendix of text or use Excel function =NORMSDIST(Z)]First find the z-scoreExample: sales force drives an average of 1200 miles, with a standard deviations of 150 miles miles is the mileage in question.
6 What is the probability that a salesperson drives less than 1600 miles? Ans: It is the area to the left of the standard normal curve. Look up 2.67 in the Table of Normal Distributions. There is a 99.62% probability that the salesperson drives less than 1600 miles.2.67
7 Using Table of the Normal Distribution Z = 2.67Table found in text page A-1 back of bookLook up 2.6 in the row, and .07 in the column.The intersection is the area to the left, or probability
9 What is the probability that a salesperson drives more than 1600 miles? 2.67Ans: It is the area to the right of the standard normal curve. Since you know the are to the left of 2.67, the area to the right must be = .0038, or .38% probability that a salesperson drives more than 1600 miles.
10 What is the probability that a salesperson drives between 1200 and 1600 miles? It is the difference between driving less than 1600 and less than 1200.2.67Ans: The area to the left of 2.67 is already known, it isFind the z value for 1200, , then look it up in the table.Between == .4962The probability that a salesperson drives between 1200 and 1600 miles is 49.62%
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