the test scores of 40 students are normally distributed with

the test scores of 40 students are normally distributed with a mean of 65

and a standard deviation of 10.

If two students are randomly selected, calculate the probability that the difference between

their scores is less than 10.

If the difference is less than 10, they are saying that it is between -10 and 10.

Thus, instead of just getting f(z), you need f(z)-f(-z)

From symmetry, of course, f(-z) = 1 - f(z)

Thus, f(z)-f(-z) = f(z) - (1-f(z)) = 2 f(z) - 1

From your value of .7611, we get close, 2(.7611) - 1 = .5222. Note that this is close, but still not the answer.

Then, if instead, we use the t distribution with 39 degrees of freedom, we get, using Excel\'s

t.dist(1/Sqrt(2),39,TRUE), a value of .758

2*.758 - 1 = .516, the provided answer.