When you have completed this chapter, you will be able to: Explain how probabilities are assigned to a continuous random variable, explain the characteristics of a normal probability distribution, define and calculate z value corresponding to any observation on a normal distribution, determine the probability a random observation is in a given interval on a normal distribution using the standard normal distribution, use the normal probability distribution to approximate the binomial probability distribution. | Continuous Probability Distributions Chapter 7 GOALS Understand the difference between discrete and continuous distributions. Compute the mean and the standard deviation for a uniform distribution. Compute probabilities by using the uniform distribution. List the characteristics of the normal probability distribution. Define and calculate z values. Determine the probability an observation is between two points on a normal probability distribution. Determine the probability an observation is above (or below) a point on a normal probability distribution. Use the normal probability distribution to approximate the binomial distribution. 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. EXAMPLE Southwest Arizona State University provides bus service to students while they are on campus. A bus arrives at the . | Continuous Probability Distributions Chapter 7 GOALS Understand the difference between discrete and continuous distributions. Compute the mean and the standard deviation for a uniform distribution. Compute probabilities by using the uniform distribution. List the characteristics of the normal probability distribution. Define and calculate z values. Determine the probability an observation is between two points on a normal probability distribution. Determine the probability an observation is above (or below) a point on a normal probability distribution. Use the normal probability distribution to approximate the binomial distribution. 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. EXAMPLE 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 . and 11 . 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. Draw a graph of this distribution. Show that the area of this uniform distribution is . 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? What is the probability a student will wait between 10 and 20 minutes? The Uniform Distribution - Example Normal Probability Distribution It is bell-shaped and has a single peak at the center of the distribution. It is symmetrical about the mean It is asymptotic: The curve gets closer and closer to the X-axis but never actually touches it. The location of a normal distribution is determined by the mean, , the dispersion or spread of the distribution is determined by the standard deviation,σ . The arithmetic mean,
