Uniform Distribution Is a continuous distribution that is evenly (or uniformly) distributed Has a density curve in the shape of a rectangle Probabilities.

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Presentation transcript:

Uniform Distribution Is a continuous distribution that is evenly (or uniformly) distributed Has a density curve in the shape of a rectangle Probabilities are calculated by finding the area under the curve Where: a & b are the endpoints of the uniform distribution

What shape does a uniform distribution have? The Citrus Sugar Company packs sugar in bags labeled 5 pounds. However, the packaging isn’t perfect and the actual weights are uniformly distributed with a mean of 4.98 pounds and a range of .12 pounds. Construct the uniform distribution above. What shape does a uniform distribution have? What is the height of this rectangle? How long is this rectangle? 1/.12 4.98 5.04 4.92

What is the length of the shaded region? What is the probability that a randomly selected bag will weigh more than 4.97 pounds? P(X > 4.97) = What is the length of the shaded region? .07(1/.12) = .5833 4.98 5.04 4.92 1/.12

What is the length of the shaded region? Find the probability that a randomly selected bag weighs between 4.93 and 5.03 pounds. What is the length of the shaded region? P(4.93<X<5.03) = .1(1/.12) = .8333 4.98 5.04 4.92 1/.12

What is the height of the rectangle? The time it takes for students to drive to school is evenly distributed with a minimum of 5 minutes and a range of 35 minutes. Draw the distribution What is the height of the rectangle? Where should the rectangle end? 1/35 5 40

b) What is the probability that it takes less than 20 minutes to drive to school? P(X < 20) = (15)(1/35) = .4286 5 40 1/35

s2 = (40 - 5)2/12 = 102.083 s = 10.104 (Standard Dev.) c) What is the mean and standard deviation of this distribution? m = (5 + 40)/2 = 22.5 s2 = (40 - 5)2/12 = 102.083 s = 10.104 (Standard Dev.)