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?

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JeanaShupp JeanaShupp · Answer 1 · 2019-11-06T07:51:50+01:00

As per given , we have

[tex]\mu=460[/tex] , [tex]\sigma= 18[/tex]

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 ([tex]\mu-1(\sigma)[/tex] and [tex]\mu+1(\sigma)[/tex])

i.e. About 68% of the observations lie between ([tex]460-1(18)[/tex] and [tex]460+1(18)[/tex])

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 ([tex]\mu-2(\sigma)[/tex] and [tex]\mu+2(\sigma)[/tex])

i.e. About 95% of the observations lie between ([tex]460-2(18)[/tex] and [tex]460+2(18)[/tex])

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 ([tex]\mu-3(\sigma)[/tex] and [tex]\mu+3(\sigma)[/tex])

i.e. Practically all of the observations lie between ([tex]460-3(18)[/tex] and [tex]460+3(18)[/tex])

Practically all of the observations lie between 406 and 514.