Question

The mean of a normal probability distribution is 460; the standard deviation is 18.About 68% of the observations lie between what two values?About 95% of the observations lie between what two values?Practically all of the observations lie between what two values?

Answer 1

Answer with explanation:

As per given , we have

$\mu=460$ , $\sigma= 18$

• According to the empirical rule , about 68% of the population lies within 1 standard deviation from mean :-

i.e. About 68% of the observations lie between ($\mu-1(\sigma)$ and $\mu+1(\sigma)$)

i.e. About 68% of the observations lie between ($460-1(18)$ and $460+1(18)$)

About 68% of the observations lie between 442 and 478.

• Again , according to the empirical rule , about 95% of the population lies within 2 standard deviations from mean :-

i.e. About 95% of the observations lie between ($\mu-2(\sigma)$ and $\mu+2(\sigma)$)

i.e. About 95% of the observations lie between ($460-2(18)$ and $460+2(18)$)

About 95% of the observations lie between 424 and 496.

• Also, Practically all of the observations(99.7%) lie between lies within 3 standard deviations from mean :-

i.e. Practically all of the observations lie between ($\mu-3(\sigma)$ and $\mu+3(\sigma)$)

i.e. Practically all of the observations lie between ($460-3(18)$ and $460+3(18)$)

Practically all of the observations lie between 406 and 514.