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01 Oct 2020, 04:15
Kudos
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
80% (01:38) correct
20%
(01:40)
wrong
based on 65
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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
Attachment:
1.png [ 11.88 KiB | Viewed 6239 times ]
01 Oct 2020, 05:56
Kudos
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Bunuel
Hi Bunuel. The diagram is not given, but I would assume it is the 68 - 96 - 100% diagram from a previous question.
(i) 68% of the values lie between 1 standard deviations below and above the mean, 34% above and 34% below.
(ii) 96% of the values lie between 2 standard deviations below and above the mean, 34% above and 34% below.
(iii) 100% of the values lie between 1 standard deviations below and above the mean, 34% above and 34% below.
71 inches is 1 standard deviation above the mean and 75 inches is 2 standard deviations above the mean.
The difference in % is 48 - 34 = 14%
Therefore the number of values that lies between these 2 values = 14% of 4000 = 560
Option B
Arun Kumar
Attachments
Normal Dist.jpg [ 272.29 KiB | Viewed 5829 times ]
