1. 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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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 =
s = (Standard Dev.)