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. |
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Sundance Kid because the distributions are uniform and his average time is better. |
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Butch Cassidy despite the fact that his average time is worse. |
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Sundance Kid despite the fact that his average time is worse. |
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The two are equally good. |
If the z-score of your midterm is -2. Choose the correct answer.
Your actual score is -2 |
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Your actual score is 2 below the average score |
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Your actual score is 2 above the average score |
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Your actual score is 2 standard deviation below the average score |
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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% |
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16% |
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84% |
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95% |
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99.7% |
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.
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%
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