Finding the Probability that Z is Between Two Numbers (# < Z < #)
1.) Look up both of the given numbers on the outside of the Standard Normal
Probabilities Table (Z-Table). For example, look up Z < 3.35 and Z< -3.35.
2.) Find the corresponding area within the table where the row and column meet for each of these numbers. These areas give the probability that Z is less than the number.
In this case, P(Z< 3.35) = .9996 and P(Z<-3.35) = .0004.
3.) To find the probability that z is between two numbers, simply subtract the smaller probability from the larger one. In this example, the probability that z is between 3.35 and -3.35 is P(-3.35 < Z < 3.35) = P(Z<3.35) – P(Z<-3.35) = .9996 – .0004 = .9992.
This is demonstrated below.
minus equals
Finding the Probability that Z is Outside Two Numbers (Z < # and Z > #)
1.) Look up both of the given numbers on the outside of the Standard Normal
Probabilities Table (Z-Table). For example, look up Z < 3.35 and Z< -3.35.
2.) Find the corresponding area within the table where the row and column meet for each of these numbers. These areas give the probability that Z is less than the number.
In this case, P(Z< 3.35) = .9996 and P(Z<-3.35) = .0004.

3.) The probability that Z is less than the smaller number has been found. To find the probability that Z is greater than the larger number, subtract the probability that Z is less than the larger number from 1. In our example,
P(Z > 3.35) = 1
– P(Z < 3.35) = 1 - .9996 = .0004
4.) To find the probability that z is less than the smaller number and greater than the larger number, add these two probabilities together. In this example, the probability that z is less than -3.35 and greater than 3.35 is P(Z < -3.35 and Z > 3.35) = P(Z < -3.35) + P( Z >3.35) = .0004 + .0004 = .0008.
This is demonstrated below. plus equals