Continuous Probability Distributions

1. Continuous Distributions
    
   1. Also known as probability distribution functions or pdf's.
       
   2. The probability of a single outcome is always zero. For instance, the probability that a person selected at random has a height of exactly 70 inches is zero. So P(X = x) = 0 always, and P(X <= x) = P(X < x) always.
       
   3. For continuous distributions we are interested in ranges of outcomes, such as "What is the probability that  person selected at random from a population is between 70 and 72 inches?"  The answer is found by calculating the area under the continuous probability distribution graph between 70 and 72.
       
2. Normal Distribution
    
   1. There are many continuous distribution functions but we will only consider the normal distribution.
       
   2. The normal distribution has two parameters, and which correspond with the population mean and population variance.

   

   3. The "standard normal distribution" is a normal distribution with mean zero and variance 1.
       
   4. If a random variable X is normally distributed with mean and variance then has the standard normal distribution.
       
   5. Use the tables in handed out in class to derive normal probabilities. The standard normal table is also available here.
       
   6. Before you can use the tables you must convert the problem into z-scores. P(X < x) = P(X < ). For instance, if  = 5 and  = 2 then P(X > 6) = P(Z > (6 - 5)/2) = P(Z > 0.5).
       
   7. Examples of how to solve normal probability problems are available here.

E-mail Mr. Callahan at stat110@edcallahan.com with questions or comments about this web site or about the class itself.