1. AP Statistics Wednesday, 06 January 2016 OBJECTIVE TSW investigate the properties of uniform distributions and normal distributions. ASSIGNMENT DUE –WS Unusual Density Curves  wire basket

2. 2 Special Continuous Distributions

3. 3 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 How do you find the area of a rectangle? Not on any formula chart – these need to be memorized!

4. 4 4.985.044.92 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 0.12 pounds. a) Construct the uniform distribution above. How long is this rectangle? What is the height of this rectangle? What shape does a uniform distribution have? 1/0.12

5. 5 What is the probability that a randomly selected bag will weigh more than 4.97 pounds? 4.985.044.92 1/0.12 P(X > 4.97) = 0.07(1/0.12) = 0.5833 What is the length of the shaded region?

6. 6 Find the probability that a randomly selected bag weighs between 4.93 and 5.03 pounds. 4.985.044.92 1/0.12 P(4.93<X<5.03) = 0.1(1/0.12) = 0.8333 What is the length of the shaded region?

7. 7 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. a) Draw the distribution 5 Where should the rectangle end? 40 What is the height of the rectangle? 1/35

8. 8 b) What is the probability that it takes less than 20 minutes to drive to school? 5 40 1/35 P(X < 20) =(15)(1/35) = 0.4286 20

9. 9 c) What is the mean and standard deviation of this distribution?  = (5 + 40)/2 = 22.5 minutes  2 = (40 - 5) 2 /12 = 102.083  = 10.104 minutes

10. ASSIGNMENT WS Uniform Distributions –Due by the end of the period today (black tray). 10