Question

The mean of a normal probability distribution is 380; the standard deviation is 16. About 68% of the observations lie between what two values

Answer 1

Solution

Given the normal distribution with

= 380 mean

= 16 standard deviation

According to the empirical rule ,

68% of the observations lie within one standard deviation from the mean.

i.e between   - and    +

i.e between 380 - 16 and 380 + 16

i.e between 364 and 396

Answer : About 68% of the observations lie between 364 and 396

(According to this rule , 95% of the observations lie within two standard deviations from the mean. i.e. between   - 2 and    + 2

99.7% ​​​​​​​ of the observations lie within three standard deviations from the mean. i.e. between   - 3 and    + 3

)