MA 132 Section 7.1 Properties of the Normal Distribution Frequency (or Probability) Distribution of Grades n What is the probability that a randomly chosen student has a grade between 50 and 59? Grade Frequency Relative • 208 Frequency 40 – 49 5 .094 50 – 59 11 .208 I 60 – 69 7 .132 70 – 79 2 .038 80 – 89 15 .283 90 – 99 13 .245 Total 53 1.000 Histogram of grades Relative Frequency 0.3 0.25 0.2 0.15 - Area 0.1 • - 208 0.05 0 40 - 49 50 - 59 60 - 69 70 - 79 80 - 89 90 - 99 What is the probability? n If we use each class as 1 unit on the x-axis, then the area of the bar representing each class is exactly the probability of a random grade being in that class. Probability Models n If we don’t have too many outcomes q q Assign a probability to each individual outcome, where the probabilities are numbers between 0 and 1 and sum to 1 The probability of any event is the sum of the probabilities of the outcomes making up the event Probability Models n If we have lots of possible outcomes q q q We can’t assign a probability to each individual outcome Probabilities are assigned to intervals of outcomes by using areas under density curves A density curve has area exactly 1 underneath it, corresponding to a total probability of 1 Normal Curves n Relative frequency histograms that are symmetric and bell-shaped are said to have the shape of a normal curve If a random variable is normally distributed, or has a normal p ...
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