Question

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?

Answer 1

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]