SOLUTION: A class of 200 students takes an exam. The students' scores are normally distributed with a mean of 72% and a standard deviation of 10. Find the number of students with scores in e
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Question 197132: A class of 200 students takes an exam. The students' scores are normally distributed with a mean of 72% and a standard deviation of 10. Find the number of students with scores in each interval.
26. between 72% and 82%
about[?] students
27. more than 92%
about[?] students
28. less than 72%
about [?] students
29. between 62% and 92%
about [?] students
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A class of 200 students takes an exam. The students' scores are normally distributed with a mean of 72% and a standard deviation of 10. Find the number of students with scores in each interval.
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I assume you mean that the standard deviation is 10%
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26.P(between 72% and 82%) = ?
Since 0.82 is 1 standard deviation to the right of 0.72 the
percentage of the population that is between those limits is
34%
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about[?] students = 0.34*200 = 68
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27. more than 92%
0.92 is 3 standard deviations to the right of the mean
The % of the population to the right of 0.92 is 2.275%
about[?] students = 0.02275*200 = 4.55
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28. less than 72%
50% of the population is to below the mean which is 0.72
about [?] students = 0.50*200 = 100
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29. between 62% and 92%
That would be 2 standard deviations to the left to two std. dev. to the right.
= 100% - 2(0.02275) = 0.9545
about [?] students = 0.9545*200 = approximately 191
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Cheers,
Stan H.
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