The mean of a normal probability distribution is 500; the standard deviation is 10.

a. about 68 percent of the observations lie between what two values?

The probability distribution table gives us

P (Z=1) = 0.8413

P (Z=-1) = 0.1586

So P (Z=1) - P (Z=-1) = 0.8413-0.1586=0.6827=68% approximately.

For Z=1 and Z-1, we have

X=mean + / - 1 * standard deviation

=500 + / - 10

=> the range is

[490,510]