The mean of a normal probability distribution is 460 the sta

Solution

Given that the mean (u) of a normal probability distribution is 460 and the
standard deviation (sd) is 10.
(a) About 68% of the area under the normal curve is within one standard deviation of the mean. i.e.
(u ± 1s.d)
So to the given normal distribution about 68% of the observations lie in between
= (460 ± 10)
= [450, 470]

(b)
About 95% of the area under the normal curve is within two standard deviations of the mean. i.e.
(u ± 2*s.d)
So to the given normal distribution about 68% of the observations lie in between
=[460 ± 2 * 10]
= 440 and 480

(c)
Practically all of the area under the normal curve is within three standard deviations of the mean. i.e.
(u ± 3*s.d)
So to the given normal distribution practically all of the observations lie in between
=[460 ± 2 * 10]
= 430 and 490