This game drills that reverse lookup. You get 10 short rounds, a running score and streak, and the correct z (with the table row and column) right after each answer.
Ten quick rounds. Each one shows a shaded area under the standard normal curve: to the left of z, to the right of z, or between −z and +z. Tap the z you think matches, or type it. Answers come straight from the z-table on our homepage.
Positive z-table · Negative z-table · How to read a z-table
Question: the shaded area to the right of z is 0.05050. What is z?
Step 1. The z-table gives left areas, so convert: 1 − 0.05050 = 0.94950.
Step 2. Find 0.94950 in the positive z-table: row 1.6, column .04.
Answer: z = 1.64. (Check: P(Z ≤ 1.64) = 0.94950, so P(Z > 1.64) = 0.05050.)
Middle-area version: if 0.95000 is shaded between −z and +z, each tail is (1 − 0.95000) / 2 = 0.02500, the left area at +z is 0.97500, and z = 1.96.
Look for the area inside the body of the z-table (the table gives the area to the left of z). Read the row label for the first decimal and the column header for the second decimal. For example, 0.97500 sits in row 1.9, column .06, so z = 1.96.
Subtract it from 1 first, because the table lists left-tail areas. A right-tail area of 0.05050 means a left area of 0.94950, which is z = 1.64.
z = 1.96. The two tails share the remaining 5%, so each tail is 0.02500 and the area to the left of +1.96 is 0.97500.
Use the closest entry in the table (the game accepts typed answers within 0.01 of the table z), or get an exact value with the z-score calculator.
Use Student's t when the population standard deviation is unknown and you estimate it from a sample, especially with small samples. Critical t values are on ttable.org, which also has a Guess the Critical t game.