Question

The mean of a normal probability distribution is 380; the standard deviation is 18. a. About 68% of the observations lie between what two values? b. About 95% of the observations lie between what two values? c. Practically all of the observations lie between what two values?

Answer 1

The 68-95-99.7 rule , also known as the empiricsl rule is as follows:

Here in this problem

So, and

So, 64% of values lies between 362 and 398

and

So, 95% values lies between 344 and 416 .

practically all values lie between the 3 limit .

and

So, practically all values lies bw 326 and 434

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As empirical rule says :   

that imples, 68% of values will lie between this range () .

Similarly the others. Thus I have got those values.