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The figure above shows a normal distribution with mean m an

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The figure above shows a normal distribution with mean m an [#permalink] New post   25 Aug 2020, 07:39
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GRE The figure above shows a normal distribution with mean m and standard deviation d.png
GRE The figure above shows a normal distribution with mean m and standard deviation d.png [ 11.88 KiB | Viewed 8392 times ]


The figure above shows a normal distribution with mean m and standard deviation d, including approximate percents of the distribution in each of the six regions shown. For a population of 4000 students in a university, the heights of these students are approximately normally distributed with a mean of 67 inches and a standard deviation of 4 inches. How many of the students had heights between 71 and 75 inches?


A. 80

B. 560

C. 1120

D. 1360

E. 1920
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Re: The figure above shows a normal distribution with mean m an [#permalink] New post   25 Aug 2020, 07:40
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Re: The figure above shows a normal distribution with mean m an [#permalink] New post   25 Aug 2020, 09:24
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Carcass wrote:
Attachment:
GRE The figure above shows a normal distribution with mean m and standard deviation d.png


The figure above shows a normal distribution with mean m and standard deviation d, including approximate percents of the distribution in each of the six regions shown. For a population of 4000 students in a university, the heights of these students are approximately normally distributed with a mean of 67 inches and a standard deviation of 4 inches. How many of the students had heights between 71 and 75 inches?

A. 80
B. 560
C. 1120
D. 1360
E. 1920


The heights of these students are approximately normally distributed with a mean of 67 inches and a standard deviation of 4 inches.
Add this information to the diagram to get:
Image



How many of the students had heights between 71 and 75 inches?
From the diagram, we can see that 14% of the heights are between 71 and 75 inches
Image


14% of 4000 students = (0.14)(4000) = 560

Answer: B

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Re: The figure above shows a normal distribution with mean m an [#permalink] New post   25 Aug 2020, 09:30
Carcass wrote:
Attachment:
GRE The figure above shows a normal distribution with mean m and standard deviation d.png


The figure above shows a normal distribution with mean m and standard deviation d, including approximate percents of the distribution in each of the six regions shown. For a population of 4000 students in a university, the heights of these students are approximately normally distributed with a mean of 67 inches and a standard deviation of 4 inches. How many of the students had heights between 71 and 75 inches?


A. 80

B. 560

C. 1120

D. 1360

E. 1920


We have \(m = 67\) and \(d = 4\).
Then we have \(71 = 67 + 4 = m + d\) and \(75 = 67 + 2 \cdot 4 = m + 2 \cdot d\).
Thus the proportion between \(71\) and \(75\) is the proportion between \(m + d\) and \(m + 2d\), which is \(14 \%\).
\(14 \%\) of \(4000\) is \(560\).

Therefore, B is the right answer.
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The figure above shows a normal distribution with mean m an [#permalink] New post   13 Aug 2023, 00:02
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The mean height is given as 67 inches and the standard deviation d is given as 4 inches. The interval between 71 and 75 inches is the interval between one and two standard deviations to the right of the mean. Since it is a normal distribution, 14% of the heights fall in this interval. That is 14% of 4000 students will have heights between 71 and 75 inches. That would be (14/100)* 4000 = 560 students. The answer is Choice B.
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