Let X be the amount in claims (in dollars) that a randomly chosen policyholder collects from an insurance company this year. The probability distribution function of X is given below.
-Let $S be the standard deviation of X. Which of the following is a correct interpretation of this value?
A) We would expect a randomly chosen policyholder to collect $S in claims this year.
B) The most likely value for the amount in claims is $S.
C) If we were to observe a large number of policyholders, the average amount claimed would be around $S.
D) On average, the amount claimed is about $S away from the mean.

Question

Let X be the amount in claims (in dollars) that a randomly chosen policyholder collects from an insurance company this year. The probability distribution function of X is given below. 
-Let $S be the standard deviation of X. Which of the following is a correct interpretation of this value?
A) We would expect a randomly chosen policyholder to collect $S in claims this year. 
B) The most likely value for the amount in claims is $S. 
C) If we were to observe a large number of policyholders, the average amount claimed would be around $S. 
D) On average, the amount claimed is about $S away from the mean.

Quizplus · Accepted Answer

The standard deviation measures the average distance of each data point from the mean, so it indicates how much the values typically deviate from the mean.

Let X Be the Amount in Claims (In Dollars) That