Carl Pride

Parent (trying to help son with home work)

suppose that in a statistics class of size 23, each student has a probability of passing of 73 percent.

sample:

What is the expected number of students who will pass??

What is the expected number of students three on either side of the expected value??

Not sure what formula to use or how to show in a graph.

You need to recognize that this is a binomial distribution, sometimes called repeated independent trials. The distinguishing features of a binomial experiment are:

0. A "simple" experiment where the outcome is one of two possibilities, called success or failure. This is a single student taking the class, he either passes or fails.
    
   
1. The "simple" experiment is repeated n times, these are called trials. Here n = 23, the number of students in the class.
    
   
2. On each trial the probability of success, p, is the same. In your example if success is passing the class then p = 0.73. The probability of any particular student passing is 0.73. This probability is independent of how the other students perform.

In a binomial experiment the expected number of successes is np. In your son's problem this is 23(0.73) = 16.79.

From here on I am not sure how to proceed, it depends very much on what they have been doing in class or what is in the textbook. I suggest that you look in his textbook for the section on binomial experiments, or repeated indepentent trials, or perhaps it is called Bernoulli trials.