Question

If the z-score of your midterm is -2. Choose the correct answer.

		Your actual score is -2
		Your actual score is 2 below the average score
		Your actual score is 2 above the average score
		Your actual score is 2 standard deviation below the average score
		Your actual score is 2 standard deviation above the average score

Your score in a recent test was 1 standard deviation above the average, what percentage of people scored lower than you did?

		68%
		16%
		84%
		95%
		99.7%

The time Butch Cassidy and Sundance Kid can run 60 yards is random and depends on the day. The time is measured in seconds. For Butch Cassidy it is a continuous random variable with f(x) = 1 for 6.4 ≤ x ≤ 7.4, and for Sundance Kid it is a continuous random variable with f(x) = 5/3 for 6.7 ≤ x ≤ 7.3. Etta Place thinks that the one who has more chances to run 60 yards faster than 7.2 seconds is a better athlete. Who of the two is a better athlete in her opinion?

		Butch Cassidy because the distributions are uniform and his average time is better.
		Sundance Kid because the distributions are uniform and his average time is better.
		Butch Cassidy despite the fact that his average time is worse.
		Sundance Kid despite the fact that his average time is worse.
		The two are equally good.

Answer 1

If the z-score of your midterm is -2. then

Your actual score is 2 standard deviation below the average score

Z score for 1 standard deviation above the average is +1.

From the standard normal table, P(Z 1) = 0.84 = 84%

The percentage of people scored lower than you did is 84%

For Butch Cassidy ,

f(x) = 1 for 6.4 ≤ x ≤ 7.4,

P(X > 7.2) =

Average time = = 6.9

For Sundance Kid,

f(x) = 5/3 for 6.7 ≤ x ≤ 7.3

P(X > 7.2) =

Average time = = 6.9

Thus, the correct oprtion is,

Butch Cassidy despite the fact that his average time is worse.