On a test that has a normal distribution, a score of 63 falls three standard deviations below the mean, and a score of 73 falls two standard deviations above the mean. Determine the mean of this test.
To determine the mean of the test, we can use the following formula:
Mean + 3 standard deviations = 63
Mean + 2 standard deviations = 73
Let's solve for the mean:
Mean + 3(Standard Deviation) = 63
Mean + 3 × (73 - Mean) = 63
Mean + 219 - 3Mean = 63
219 - 2Mean = 63
2Mean = 156
Mean = 78
Therefore, the mean of the test is 78.