Question

Which of the following is the standard deviation of the random variable x, the number that appears on a fair, 10-sided die, if the probability of any number on a fair, 10-sided die is 1/10?

A) 5.2
B) 3.028
C) 2.872
D) 0.1

Answer 1

The standard deviation of the random variable for a 10-sided die is found by calculating the mean, determining the variance, and then taking the square root of the variance, resulting in a standard deviation of approximately 2.872.

Step-by-step explanation:

To find the standard deviation of a random variable representing the number that appears on a fair, 10-sided die, we must first calculate the expected value (mean) and then use it to find the variance and the standard deviation. The faces of a 10-sided die are numbered 1 through 10, so the mean is calculated as the sum of these numbers divided by the number of sides:

Mean (µ) = (1+2+3+4+5+6+7+8+9+10)/10 = 5.5

To find the variance (σ2), we calculate the sum of the squared differences between each outcome and the mean, and then divide by the number of sides:

Variance (σ2) = [(1-5.5)2 + (2-5.5)2 + ... + (10-5.5)2]/10
= 8.25

Finally, the standard deviation (σ) is the square root of the variance:

Standard deviation (σ) = √8.25 ≈ 2.872

Therefore, the correct answer to the student's question is C) 2.872.