MGMT 2340 Section W01 Business Statistics I Instructor: E. Mark Leany contact via Blackboard online.uen.org alternately: [email protected] Continuous Probability Distributions Chapter 7 218
GOALS 1. Understand the difference between discrete and continuous distributions. 2. Compute the mean and the standard deviation for a uniform distribution . 3. Compute probabilities by using the uniform distribution. 4. List the characteristics of the normal probability distribution . 5. Define and calculate z values. 6. Determine the probability an observation is between two points on a normal probability distribution. 7. Determine the probability an observation is above (or below) a point on a normal probability distribution. 8. Use the normal probability distribution to approximate the binomial distribution. 218 Binomial – Shapes for Varying n ( S constant) 197 Total Area = 1.00 Area = Height x Width = Probability
The Uniform Distribution The uniform probability distribution is perhaps the simplest distribution for a continuous random variable . This distribution is rectangular in shape and is defined by minimum and maximum values. Events are Equally Likely (hence Uniform) What do we know about area? Sum of Area = 1 219 Area of a Line = 0.00 The Uniform Distribution – Mean and Standard Deviation 220
Southwest Arizona State University provides bus service to students while they are on campus. A bus arrives at the North Main Street and College Drive stop every 30 minutes between 6 A.M. and 11 P.M. during weekdays. Students arrive at the bus stop at random times. The time that a student waits is uniformly distributed from 0 to 30 minutes. 1. Draw a graph of this distribution. 2. Show that the area of this uniform distribution is 1.00. 3. How long will a student “typically” have to wait for a bus? In other words what is the mean waiting time? 4. What is the standard deviation of the waiting times? 5. What is the probability a student will wait more than 25 minutes 6. What is the probability a student will wait between 10 and 20 minutes? The Uniform Distribution - Example 221 The Uniform Distribution - Example 1. Draw a graph of this distribution. 221 3 0 . 0 0 30 1 1 ) ( ! 0 ! 0 ! a b x P
The Uniform Distribution - Example 2. Show that the area of this distribution is 1.00 221 The Uniform Distribution - Example 3. How long will a student “typically” have to wait for a bus? In other words what is the mean waiting time? What is the standard deviation of the waiting times? 221
The Uniform Distribution - Example 4. What is the probability a student will wait more than 25 minutes?
- Spring '11
- Normal Distribution