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# Justin took a test of French at school and scored 72 marks out of 100.

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Justin took a test of French at school and scored 72 marks out of 100.  [#permalink]

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24 Mar 2019, 11:15
1
00:00

Difficulty:

75% (hard)

Question Stats:

39% (01:56) correct 61% (01:52) wrong based on 28 sessions

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Justin took a test of French at school and scored 72 marks out of 100. If there were 20 students who appeared for the test, within how many standard deviations from the mean did Justin’s score lie?

(1) Darren and Matthew scored 70 and 75 respectively and their scores were within one standard deviation from the mean.
(2) The mean score of 20 students was 65 and Andrew who scored 59 was within one standard deviation of the mean.

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Re: Justin took a test of French at school and scored 72 marks out of 100.  [#permalink]

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29 Mar 2019, 08:12
PriyankaPalit7 wrote:
Justin took a test of French at school and scored 72 marks out of 100. If there were 20 students who appeared for the test, within how many standard deviations from the mean did Justin’s score lie?

(1) Darren and Matthew scored 70 and 75 respectively and their scores were within one standard deviation from the mean.
(2) The mean score of 20 students was 65 and Andrew who scored 59 was within one standard deviation of the mean.

Questions involving std and variance are almost always solved based on basic logical properties (without calculation).
We'll look for such a solution, a Logical approach.

(1) Let the mean be x. If x < 70, then since x < 72 < 75 and 75 is within 1 std then so is 72. Similar logic holds for x > 75 and for 72 < x < 75, and therefore the answer is always 1.
Sufficient.

(2) So since 59 = 65 - 6 is within 1 std, then so is 71 = 65 + 6. But we need to know if 72, and not 71, is within 1 std (or more), so this is not enough.
Insufficient.

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Re: Justin took a test of French at school and scored 72 marks out of 100.   [#permalink] 29 Mar 2019, 08:12
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