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by Anju@Gurome » Sun Apr 21, 2013 11:11 am
puneet2329 wrote:9.4, 9.9, 9.9, 9.9, 10.0, 10.2, 10.2, and 10.5
The mean and standard deviation of the above 8 numbers are 10.0 and 0.3 respectively. What percent of the 8 numbers are within 1 standard deviation of the mean?
A. 90%
B. 85%
C. 80%
D. 75%
E. 70%

Mean = 10 and Standard Deviation, S.D = 0.3
1 S.D. of the mean = 1*0.3 = 0.3
Mean - S.D = 10 - 0.3 = 9.7, which is the lower limit
Mean + S.D. = 10 + 0.3 = 10.3, which is upper limit

We can see that only 6 out of the 8 given numbers, lie between 9.7 and 10.3.
So, percent of the 8 numbers that are within 1 standard deviation of the mean = (6/8)*100 = 75%

The correct answer is D
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