Q. 3.126 - Elementary Statistics

Question

The data set has size$60$ . Approximately how many observations lie within three standard deviations to either side of the mean? 

Step-by-Step Solution

Answer

The observations that  lie within three standard deviations to either side of the mean approximately are $59.82$

Step 1: Given information

We are given that data set has size $60$.

Step 2: Explanation

Here we  will use Empirical Rule , for normally distributed random variable, $99.7\%$ of the measures are within two standard deviation of the mean.

We are given the size of data set to be$60$  , as here distributions are normal ,

So we get ,$0.997\times 60=59.82$

Approximately,$59.82$ observation lie within two standard deviations of the mean.