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For a group of test-takers, the scores on an aptitude test w
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17 Sep 2017, 11:53
17 Sep 2017, 11:53
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Question Stats:
84% (00:58) correct
15% (01:02) wrong based on 171 sessions
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For a group of test-takers, the scores on an aptitude test were normally distributed, had a mean of 154, and a standard deviation of 3.
Quantity A |
Quantity B |
The fraction of test-takers in the group who scored greater than 158 |
\(\frac{1}{3}\) |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
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Re: For a group of test-takers, the scores on an aptitude test w
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08 Jun 2020, 05:04
08 Jun 2020, 05:04
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Carcass wrote:
For a group of test-takers, the scores on an aptitude test were normally distributed, had a mean of 154, and a standard deviation of 3.
Quantity A |
Quantity B |
The fraction of test-takers in the group who scored greater than 158 |
\(\frac{1}{3}\) |
Here's what we know about the normal distribution:
The question tells us that the distribution has a mean of 154 and a standard deviation of 3.
Add this information to the diagram to get:
For Quantity A, we want to find the fraction of test-takers who scored GREATER THAN 158.
From our diagram we can see that 16% (14% + 2%) of the scores are greater than 157.
So, less than 16% of the scores are greater than 158
Since 16% = 16/100, we get:
QUANTITY A: Some fraction less than 16/100
QUANTITY B: 1/3
Answer: B
Cheers,
Brent
General Discussion
Re: For a group of test-takers, the scores on an aptitude test w
[#permalink]
17 Sep 2017, 23:26
17 Sep 2017, 23:26
2
Is this based on the fact that each half of the normal distribution contains 0.5 probability and that the probability between the mean and 1sd, 2sd and 3sd is known to be, respectively, 0.34, 0.136 and 0,023? Thus, given that 158 is a number more than 1sd from the mean, the probability of lying there should be equal to 0.136+0.023=0.158 so less than 1/3 that is roughly 0.333. Thus, answer is B.
