Combining Random Variables

Rory and Kealan are bowlers whose scores are approximately normally distributed. Rory has an average score of 210 points and standard deviation of 7 points. Keelan has an average score of 250 points with a standard deviation of 15 points. When they play together as a team, their combined scores are approximately normally distributed. What is the mean and standard deviation, respectively, of their combined scores?

• 460; 274

• 40; 22

• 230, 16.55

• 460; 16.55

• 460; 22

A random variable X has a mean of 120 and a standard deviation of 15. A random variable Y has a mean of 100 and a standard deviation of 9. If X and Y are independent, approximately what is the standard deviation of X – Y?

• 24.0

• 17.5

• 12.0

• 6.0

• 4.9

Tags

CCSS.HSS.ID.A.2

CCSS.HSS.ID.A.4

The amount of food eaten in a day is approximately normally distributed. For brunch, Charles can eat a mean of 1 pounds of food with a standard deviation of .18 pounds. For dinner, he can eat a mean of 1.5 pounds with a standard deviation of .23 pounds. What is the probability that he eats at least 3 pounds of food in a day?

• cannot be determined from the given information

• 0.0423

• 0.1113

• 0.8887

• 0.9577

Rory and Kealan are bowlers whose scores are approximately normally distributed. Rory has an average score of 230 points and standard deviation of 7 points. Keelan has an average score of 250 points with a standard deviation of 15 points. When they play against each other, their differences in scores are approximately normally distributed. What is the probability that Rory beats Keelan?

• 0.1134

• 0.8866

• 0.1817

• 0.8183

• None of the above