On a test that has a normal distribution, a score of 78 falls one standard deviation above the mean, and a score of 62 falls one standard deviation below the mean. Determine the mean of this test.
To determine the mean of the test, we need to calculate the distance between the mean and one standard deviation above and below the mean.
Let x be the mean of the test.
Given:
78 = x + 1 standard deviation
62 = x - 1 standard deviation
Solving for x using the above equations:
x + standard deviation = 78
x = 78 - standard deviation
x - standard deviation = 62
78 - standard deviation - standard deviation = 62
78 - 2*standard deviation = 62
78 = 62 + 2*standard deviation
16 = 2*standard deviation
standard deviation = 8
Substitute the standard deviation back into the first equation to solve for x:
x = 78 - 8
x = 70
Therefore, the mean of this test is 70.