Occasionally we can avoid the binomial formula. Our text has probability distributions for the binomial distribution already worked out. The values of n range from 1 to 20, and the values of p that are included are 0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 and 0.95. So, if the value of n is less than or equal to 20 and the value of p is one of the 12 values listed above, you should use the tables. The calculations are done for you, and all you have to be able to do is read a table. You should only resort to the formula if you can not use the tables.
Ex. The probability that a student that received a C in a math
class goes on to receive a C or better in their next math class
is 0.1. If 5 students in a class receive C's, find the probability
that 3 of them go on to receive a C or better in their next math
class.
n = 5 and p = 0.1, so we can use the table. Here's
what it looks like.
n = 5
Once you've identified the proper table for your value of n,
go down to the row that corresponds to the correct value of x.
n = 5
Then go across to the column that corresponds to the value of
p. Where this column crosses the row for x, you'll
find the probability.
n = 5
The tables tell us the probability is 0.008, we calculated it to be 0.0081. Which do you find to be easier? If you still prefer the formula, consider the following problem.
Ex. The probability that a student that received a C in a math
class goes on to receive a C or better in their next math class
is 0.1. If 5 students in a class receive C's, find the probability
that at least 1 of them go on to receive a C or better in their
next math class.
Much easier that using the formula 5 different times. Of course,
we could have used the following strategy as well.
The answer is a little different, due to the table's use of rounding.