Question

Sisters Amilia and Bianca play games together often. Let A represent the number of games Amilia wins monthly, and let B represent the number of games Bianca wins monthly. A and B are independent events. The mean of A is 35. 7 games with a standard deviation of 5. 1 games, and the mean of B is 37. 3 games with a standard deviation of 6. 8 games. What is the mean and standard deviation of the total number of games won, S = A + B? Mu Subscript s = 54. 4 games and Sigma Subscript s= 3. 4 games. Mu Subscript s = 54. 4 games and Sigma Subscript s= 11. 9 games. Mu Subscript s = 73. 0 games and Sigma Subscript s= 8. 5 games. Mu Subscript s = 73. 0 games and Sigma Subscript s= 11. 9 games

Answer 1

Using addition of variables, it is found that the mean of S is of 73 and the standard deviation is of 8.5.

What happens to the mean and the standard deviation when two variables are added?

• The mean is the sum of the means.

• The standard deviation is the square root of the sum of variances.

In this problem, for variables A and B, we have that:

$\mu_A = 35.5, \sigma_A = 5.1$

$\mu_B = 37.3, \sigma_B = 6.8$

Variable S is the sum of A and B, hence:

$\mu_S = \mu_A + \mu_B = 35.5 + 37.3 = 73$

$\sigma_S = \sqrt{\sigma_A^2 + \sigma_B^2} = \sqrt{5.1^2 + 6.8^2} = 8.5$

The mean of S is of 73 and the standard deviation is of 8.5.

More can be learned about addition of variables at https://brainly.com/question/26156502