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

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Menna
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The salary scale for players in a certain sports league is d [#permalink] New post   Updated on: 14 Jul 2018, 11:19
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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



Cambridge, Victory book.
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D

Originally posted by Menna on 14 Jul 2018, 10:16.
Last edited by Menna on 14 Jul 2018, 11:19, edited 2 times in total.
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Re: Standard Deviation Question [#permalink] New post   14 Jul 2018, 11:16
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Is this a numeric entry question or a problem solving with five answer choices ??

Please post the question properly, so we can help you @Menna.

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Re: The salary scale for players in a certain sports league is d [#permalink] New post   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
bell curve.png [ 7.13 KiB | Viewed 3041 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
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Re: The salary scale for players in a certain sports league is d [#permalink] New post   15 Jul 2018, 23:01
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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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Re: The salary scale for players in a certain sports league is d [#permalink] New post   16 Jul 2018, 11:45
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It appears to be recording the correct answer (d) as incorrect. Please fix :shock:
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Re: The salary scale for players in a certain sports league is d [#permalink] New post   16 Jul 2018, 12:57
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Fixed as D.

Thank you.

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Re: The salary scale for players in a certain sports league is d [#permalink] New post   11 Jan 2019, 09:14
Menna wrote:
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.

Please remove the answer shown.
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Re: The salary scale for players in a certain sports league is d [#permalink] New post   12 Jan 2019, 01:31
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Done
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Re: The salary scale for players in a certain sports league is d [#permalink] New post   13 Jun 2022, 01:56
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Re: The salary scale for players in a certain sports league is d [#permalink]
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