Question

Two random variables, X and Y, have standard deviations 2.4 and 3.6, respectively. Which one is more likely to take a value close to its mean? Explain your answer.

Short answer

X is more likely to take a value close to its mean.

Step-by-step solution

Step 1. Given information.

The given statement is:

Two random variables, Xand Y, have standard deviations of 2.4 and 3.6, respectively.

Step 2. Determine the value close to its mean.

For any two random variables, the one with a lower standard deviation than the other's mean will take a value near to that of the other.

The random variable X has a lower mean than the random variable Y's standard deviation.

Because random variable X has a lower standard deviation than random variableY, it is more likely to take a value nearer to the mean.