Question

The mean of a normal probability distribution is 380; the standard deviation is 10.

a. About 68% of the observations lie between what two values?

2. About 95% of the observations lie between what two values?

3. Practically all of the observations lie between what two values?

Answer 1

a. 68% of the observations lie between the z scores of -1 to +1

Now, z= X - mean/s.d

So, here X= +-1*S.D + mean

So X = 370, 390

Hence 68% of the values lie between 370 to 390

b. 95% of the values lie between z-score of +-1.96

So, here X= +-1.96*10 + 380

So X= 360.4, 399.6

So 95% of the values lie between 360.4 to 399.6

c. About 100% of the values should lie between the z score of +-3

So, X= 350, 410

So practically all the values should lie between 350 to 410