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Corporation X pays $6,300,000 in salary to its 150 employees and indiv 29 Mar 2017, 04:56
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75% (hard)

Question Stats:

20% (01:23) correct 80% (02:26) wrong based on 10 sessions

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Corporation X pays $6,300,000 in salary to its 150 employees and individual salaries have a normal distribution. If the standard deviation in the salaries is $12,000, which of the following could be the total amount paid in salary to the top 3 employees?

A. $42,000
B. $66,000
C. $132,000
D. $196,000
E. $264,000



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E
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Corporation X pays $6,300,000 in salary to its 150 employees and indiv 29 Mar 2017, 11:19
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Bunuel
Corporation X pays $6,300,000 in salary to its 150 employees and individual salaries have a normal distribution. If the standard deviation in the salaries is $12,000, which of the following could be the total amount paid in salary to the top 3 employees?

A. $42,000
B. $66,000
C. $132,000
D. $196,000
E. $264,000


avg salary paid =6300000/150 = 42000
SD = 12000
thus max. of salary will be = 42000+12000= 54000
and minimum of high salary be = 42000

thus salary of 3 high employees must be 3*4200< S<3*54000
where s is required sum
thus
12600<s< 162000
only option C falls in range, thus
Ans C
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Corporation X pays $6,300,000 in salary to its 150 employees and indiv 29 Mar 2017, 11:31
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Mean value = 42000
maximum can be 42000+12000=54000

Thus maximum sum of highest 3 can be 54000*3=162000

Thus our answer will be number = 162000 or an option lower than 162000 and closest to 162000

thus, C is correct answer
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Corporation X pays $6,300,000 in salary to its 150 employees and indiv 05 Apr 2017, 14:37
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I think the answer is E.

Derived from assuming that among normally distributed 150 employees, 2%, or 3 people, will be in >SD +2 to SD +3 range, $66,000.01 to $78,000. Only answer E is big enough. Look for max/min to test answer limits. Max: $78,000 x 3 = $234,000.

Min: If normally distributed, even if all three earn the lowest end of SD +3 range, it doesn't work; i.e., $66,000.01 x 3 = $198,000.03, which is greater than D.

Mean is $42,000. ($6.3M/150)

Mean + 1SD = $54,000, at about 84th percentile.

Mean + 2SD = $66,000, at about 98th percentile.

Mean + 3SD = $78,000, at 100th percentile.

What am I missing? Why does the maximum salary stop at one standard deviation above the mean if salaries are normally distributed and there are 150 people? I'm lost!

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Corporation X pays $6,300,000 in salary to its 150 employees and indiv 05 Apr 2017, 21:11
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Bunuel
Corporation X pays $6,300,000 in salary to its 150 employees and individual salaries have a normal distribution. If the standard deviation in the salaries is $12,000, which of the following could be the total amount paid in salary to the top 3 employees?

A. $42,000
B. $66,000
C. $132,000
D. $196,000
E. $264,000


Hi Bunuel,

Could you please explain the OA?



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