Question

The mean of a normal probability distribution is 340; the standard deviation is 12.

1. 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)

As per empirical rule, about 68% observations are within 1 - standard deviation from the mean

lower limit = 340 - 12 = 328

upper limit = 340 + 12 = 352

b)

As per empirical rule, about 95% observations are within 2 - standard deviation from the mean

lower limit = 340 - 2*12 = 316

upper limit = 340 + 2*12 = 364

c)

As per empirical rule, about 99.7% observations are within 3 - standard deviation from the mean

lower limit = 340 - 3*12 = 304

upper limit = 340 + 3*12 = 376