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11 Jan 2021, 08:41
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D
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Difficulty:
95%
(hard)
Question Stats:
34% (01:56) correct
66%
(01:59)
wrong
based on 83
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Not Attempted Yet
For the numbers 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, and 105, if m represents the mean and d represents the standard deviation, how many are greater than m - d and less than m + d?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
XSatishX
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11 Jan 2021, 09:15
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Not Sure but I read it somewhere that 68 % of data in a set lies within 1 standard deviation. This question is basically asking the same. How many elements lie within 1 standard deviation.
68% of 12 = 68/100*12 = 8.16 ~ 8
Hence answer is 8
68% of 12 = 68/100*12 = 8.16 ~ 8
Hence answer is 8
11 Jan 2021, 10:56
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Numbers are 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, and 105.
There are 13 numbers. Mean = 100 (mid number for equidistant odd distribution)
Standard deviation = Sqrt [{(100-95)^2 + (100-96)^2 + (100-97)^2 + (100-98)^2 + (100-99)^2}*2/11] = Sqrt (10)
greater than m-d = 100- 3.16 = 96.84, it will be 97, 98, 99, 100, 101, 102, 103, 104, and 105.
less than m+d = 100+3.16 = 103.16, it will be 95, 96, 97, 98, 99, 100, 101, 102 and 103.
So, there will 7 values. I think D.
There are 13 numbers. Mean = 100 (mid number for equidistant odd distribution)
Standard deviation = Sqrt [{(100-95)^2 + (100-96)^2 + (100-97)^2 + (100-98)^2 + (100-99)^2}*2/11] = Sqrt (10)
greater than m-d = 100- 3.16 = 96.84, it will be 97, 98, 99, 100, 101, 102, 103, 104, and 105.
less than m+d = 100+3.16 = 103.16, it will be 95, 96, 97, 98, 99, 100, 101, 102 and 103.
So, there will 7 values. I think D.
