Chapter 6.3, Problem 119E

To determine

To find: the rank of the three random variables from the smallest to largest on the basis of standard deviations.

Answer to Problem 119E

B, C, A

Explanation of Solution

Given:

  

The standard deviation computes the average deviation of the data values with respect to the mean $\mu$ .

This then means that if more number of data values lie closest to $\mu$ , then the standard deviation would be smaller.

The standard deviation of B is then smallest, because of the peak of the density curve is the highest at $\mu$ and therefore the most of the data values lie very close to the means $\mu$ .

The standard deviation of A is largest, because of the peak of the density curve is the highest at the points furthest from the mean $\mu$ and therefore the most of the data values lie far away from the mean $\mu$ .

Therefore the standard deviations from smallest to largest is B, C, A.