Z Score Table Sample Problems
Use these sample zscore math problems to help you learn the zscore formula.
What is P (Z ≤ 1.5) ?
Answer: 0.9332
To find the answer using the Ztable, find where the row for 1.5 intersects with the column for 0.00; this value is 0.9332. The Ztable shows only "less than" probabilities so it gives you exactly what you need for this question. Note: No probability is exactly at one single point, so:
P (Z ≤ 1.5) = P (Z < 1.5) 
What is P (Z ≥ 1.5) ?
Answer: 0.0668
Use the Ztable to find where the row for 1.5 intersects with the column for 0.00, which is 0.9332. Because the Ztable gives you only "less than" probabilities, subtract P(Z < 1.5) from 1 (remember that the total probability for the normal distribution is 1.00, or 100%):
P (Z ≥ 1.5) = 1 – P (Z < 1.5)= 1 – 0.9332 = 0.0668

What is P (–0.5 ≤ Z ≤ 1.0) ?
Answer: 0.5328
To find the probability that Z is between two values, use the Ztable to find the probabilities corresponding to each zvalue, and then find the difference between the probabilities.
Here, you want the probability that Z is between –0.5 and 1.0. First, use the Ztable to find the value where the row for –0.5 intersects with the column for 0.00, which is 0.3085. Then, find the value where the row for 1.0 intersects with the column for 0.00, which is 0.8413.
Because the Ztable gives you only "less than" probabilities, find the difference between the probability less than 1.0 and the probability less than –0.5:
P (–0.5 ≤ Z ≤ 1.0) = P (Z ≤ 1.0) – P (Z ≤ –0.50)= 0.8413 – 0.3085 = 0.5328

What is P (–1.0 ≤ Z ≤ 1.0) ?
Answer: 0.6826
To find the probability that Z is between two values, use the Ztable to find the probabilities corresponding to each zvalue, and then find the difference between the probabilities.
Here, you want the probability that Z is between –1.0 and 1.0. First, use the Ztable to find the value where the row for –1.0 intersects with 0.00, which is 0.1587. Then, find the value where the row for 1.0 intersects with the column for 0.00, which is 0.8413.
Because the Ztable gives you only "less than" probabilities, find the difference between probability less than 1.0 and the probability less than –1.0:
P (–1.0 ≤ Z ≤ 1.0) = P (Z ≤ 1.0) – P (Z ≤ –1.0)= 0.8413 – 0.1587 = 0.6826