Section 5.2: PROBABILITY AND THE NORMAL DISTRIBUTION.

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Presentation transcript:

Section 5.2: PROBABILITY AND THE NORMAL DISTRIBUTION

Objective: To be able to find probabilities based on the normal distribution using the tables and technology. Steps for finding probability when given a random variable X 1.Convert from X to Z by using the z-score formula. 2.Classify the problem as area to the right, left or between. 3.Use the proper technique using tables or the calculator to find the solution. Ex. 1. Let X = the height of an adult woman. If X has a mean of 64.5 and a standard deviation of 2.5, then find the following: a. P(X < 64.5)

b. P(X < 62) c. P(X < 60.5) d. P(X < 67.3) e. P(X > 70.25) f. P(X > 64.35)

g. P(61 < X < 65.3) h. P(66.24 < X < 71.45) i. P(58.33 < X < 62.87) j. P(X = 62)

Ex. 2 Let X = the time is takes for a student to get to class at MHS. If the mean is 270 seconds and the standard deviation is 27 seconds, find the probability that a.It takes less than 4 minutes to get to class. b.It takes no more than 310 seconds. c.It takes at least 5 minutes

d. It takes no less than 6 minutes. e. It takes between 4.5 and 5.5 minutes. f. It takes between 6 and 7 minutes. g. It takes exactly 5.5 minutes