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.