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The 500 students in a class took an examination. Sco
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22 Aug 2017, 02:16
22 Aug 2017, 02:16
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Question Stats:
23% (02:04) correct
76% (02:22) wrong based on 158 sessions
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The 500 students in a class took an examination. Scores were given on an integer scale of 0-100. Jamal's score was 2 standard deviations above the mean score on the examination, and Charlie's score was at exactly the 5th percentile. The distribution of exam scores was approximately normal. Which of the following statements must be true?
Indicate all such statements.
❑ Jamal scored closer to the mean than Charlie.
❑ More than 400 students achieved scores less than or equal to Jamal's score and greater than or equal to Charlie's score.
❑ Fewer than 450 students achieved scores less than or equal to Jamal's score and greater than or equal to Charlie's score.
❑ At least one other person received the same score as Charlie.
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Re: The 500 students in a class took an examination. Sco
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23 Apr 2018, 19:00
23 Apr 2018, 19:00
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A:
You need to know that in a normal curve, the mean is exactly at the 50%ile, 1 standard deviation above the mean is 34%ile above that, and 2 standard deviations above the mean is 14%ile above that. In other words, 2 standard deviations above the mean is around 98%ile. Since Jamal is therefore at 98%ile and Charlie as at 5%ile, Charlie is closer to the mean and this answer is out.
B:
If Charlie is 5%ile, then he performed better than 5% of the total, or 25 people. Since Jamal is 98%ile, he performed better than 98% of the students, meaning about 2% of them, about 10 students, performed better than him. Since only about 35 people out of 500 performed either better or worse than them, 465 must have performed equal to Charlie or above or equal to Jamal or below, so we can see that this answer must be true.
C:
From the last answer choice, we know that we're looking at 465 people, which is well above 450, so this one is out.
D:
Since there are 500 students, every percentile must contain 5 students. The key to this one is the word "exactly". Since the 5th percentile falls between the 25th and 26th student, the 5th percentile itself is the average of the 25th and 26th students' scores. Since the scores are given in integers, if you average two of them, you'll either get an integer, or something that ends in a .5. But since Charlie couldn't have gotten a score that ends in a .5, this scenario is out.
What if the 25th lowest student had scored a 20 and the 26th lowest had gotten a 22? Then the 5th percentile would be 21, but since nobody actually got that score, this scenario is impossible.
The only way Charlie could've gotten exactly the 5th percentile is if the 25th and 26th lowest people got the same score, in which case the average of the two of them equals both of them. Thus, D is in.
You need to know that in a normal curve, the mean is exactly at the 50%ile, 1 standard deviation above the mean is 34%ile above that, and 2 standard deviations above the mean is 14%ile above that. In other words, 2 standard deviations above the mean is around 98%ile. Since Jamal is therefore at 98%ile and Charlie as at 5%ile, Charlie is closer to the mean and this answer is out.
B:
If Charlie is 5%ile, then he performed better than 5% of the total, or 25 people. Since Jamal is 98%ile, he performed better than 98% of the students, meaning about 2% of them, about 10 students, performed better than him. Since only about 35 people out of 500 performed either better or worse than them, 465 must have performed equal to Charlie or above or equal to Jamal or below, so we can see that this answer must be true.
C:
From the last answer choice, we know that we're looking at 465 people, which is well above 450, so this one is out.
D:
Since there are 500 students, every percentile must contain 5 students. The key to this one is the word "exactly". Since the 5th percentile falls between the 25th and 26th student, the 5th percentile itself is the average of the 25th and 26th students' scores. Since the scores are given in integers, if you average two of them, you'll either get an integer, or something that ends in a .5. But since Charlie couldn't have gotten a score that ends in a .5, this scenario is out.
What if the 25th lowest student had scored a 20 and the 26th lowest had gotten a 22? Then the 5th percentile would be 21, but since nobody actually got that score, this scenario is impossible.
The only way Charlie could've gotten exactly the 5th percentile is if the 25th and 26th lowest people got the same score, in which case the average of the two of them equals both of them. Thus, D is in.
General Discussion
Re: The 500 students in a class took an examination. Sco
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24 Apr 2018, 01:45
24 Apr 2018, 01:45
Expert Reply
Amazin explanation. As usual.
I missed it.
I missed it.
