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# The salary scale for players in a certain sports league is d

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The salary scale for players in a certain sports league is d [#permalink]  14 Jul 2018, 10:16
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The salary scale for players in a certain sports league is determined statistically by reference to a curve with a normal distribution. In 1960, the mean salary for players in the league was $10,000 with a standard deviation of$1000. That year,rookie players were paid $8,000. In 2010, the mean salary for players in the league was 1,175,000 with a standard deviation of$300,000. Rookies in 2010 were paid salaries in a dollar amount equal to a position on normal curve for 2010 that rookie players were paid in the year 1960. What was the salary for rookie players in 2010?

A- $1,475,000 B-$1,175,000
C- $875,000 D-$575,000
E- $275,000 OA:$575,000

Cambridge, Victory book.
[Reveal] Spoiler: OA

Last edited by Menna on 14 Jul 2018, 11:19, edited 2 times in total.
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Re: Standard Deviation Question [#permalink]  14 Jul 2018, 11:16
Expert's post
Is this a numeric entry question or a problem solving with five answer choices ??

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Re: The salary scale for players in a certain sports league is d [#permalink]  15 Jul 2018, 02:35
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The trick in this question is not to get intimidated by the terms mean and standard deviation.

Mean is the salary the guy at 50th percentile gets. So let us suppose we have 100 guys in the league and we make them stand in a row with increasing salary then the guy standing in the 50th position in the line get the mean salary.

So 50th guy in the line will get $10000 in 1960 So 50th guy in the line will get$1175000 in 2010.

Look at the curve below. One standard deviation means that the guys at 84.13 (50% +34.13%) earn more and and guys at 15.87% (50% - 34.13%) earn less by the amount of standard deviation.

Attachment:

bell curve.png [ 7.13 KiB | Viewed 365 times ]

So in 1960 the guys earning $10000 were at 50% guys earning$9000 ($10000-$1000) were at the 15.87% and guys earning $8000 ($10000-2*$1000) were at 2.28%. The question suggest the all the rookie players were in the last 2.28% of the population. So apply the distribution to the new salaries we can say that rookies in 2010 were earning two standard deviations below the average. So the rookie income in 2010 = mean income - 2 *standard devation=$1175000-$300000-$300000.=$575000 _________________ Sandy If you found this post useful, please let me know by pressing the Kudos Button Try our free Online GRE Test Director Joined: 07 Jan 2018 Posts: 553 Followers: 4 Kudos [?]: 477 [2] , given: 84 Re: The salary scale for players in a certain sports league is d [#permalink] 15 Jul 2018, 23:01 2 This post received KUDOS From the question, The Mean of 1960 is $$10000$$ while S.D. is $$1000$$ The salary of rookie player in 1960 is 2 SD below the mean which is $$10000-2000 = 8000$$ Now coming to 2010 we are given that the Mean is 1,175,000 and 1 S.D. is$300,000
Hence if the payment was commensurate with the distribution of normal curve of 1960 we can conclude that rookie players received 2 S.D. below the mean
or, $$1175000- 2 * 300,000 = 1175000 - 600000 = 575000$$
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This is my response to the question and may be incorrect. Feel free to rectify any mistakes

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Re: The salary scale for players in a certain sports league is d [#permalink]  16 Jul 2018, 11:45
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It appears to be recording the correct answer (d) as incorrect. Please fix
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Re: The salary scale for players in a certain sports league is d [#permalink]  16 Jul 2018, 12:57
Expert's post
Fixed as D.

Thank you.

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Re: The salary scale for players in a certain sports league is d   [#permalink] 16 Jul 2018, 12:57
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