Q. 3.124 - Elementary Statistics

Question

The data set has size $40$. Approximately how many observations lie within two standard deviations to either side of the mean? 

Step-by-Step Solution

Answer

The observations that  lie within two standard deviations to either side of the mean approximately are $38$.

Step 1: Given information

We are given that data set has size $40$.

Step 2: Explanation

Here we  will use Empirical Rule , for normally distributed random variable, $95\%$ of the measures are within two standard deviation of the mean.

We are given the size of data set to be$40$  , as here distributions are normal ,

So we get ,$0.95\times 40=38$

Approximately,$38$ observation lie within two standard deviations of the mean.