Statistics: 1001 Practice Problems For Dummies (+ Free Online Practice)
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You can use the Z-score table to find a full set of "less-than" probabilities for a wide range of z-values using the z-score formula. Below you will find both the positive z-score and negative z-score table. In figuring out statistics problems, make sure you understand how to use the Z-table to find the probabilities you want.

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Z Score Table Sample Problems

Use these sample z-score math problems to help you learn the z-score formula.
  1. What is P (Z ≤ 1.5) ?

    Answer: 0.9332

    To find the answer using the Z-table, find where the row for 1.5 intersects with the column for 0.00; this value is 0.9332. The Z-table 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)
  2. What is P (Z ≥ 1.5) ?

    Answer: 0.0668

    Use the Z-table to find where the row for 1.5 intersects with the column for 0.00, which is 0.9332. Because the Z-table 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

  3. What is P (–0.5 ≤ Z ≤ 1.0) ?

    Answer: 0.5328

    To find the probability that Z is between two values, use the Z-table to find the probabilities corresponding to each z-value, 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 Z-table 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 Z-table 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

  4. What is P (–1.0 ≤ Z ≤ 1.0) ?

    Answer: 0.6826

    To find the probability that Z is between two values, use the Z-table to find the probabilities corresponding to each z-value, 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 Z-table 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 Z-table 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

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