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17 Mar 2025, 00:30
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E
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Difficulty:
25%
(medium)
Question Stats:
73% (01:11) correct
27%
(01:53)
wrong
based on 96
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If the mean of list A is 6.8 and the standard deviation is 3.6, then how many elements of list A are within 1 unit of standard deviation of the mean?
A = {2, 9, 2, 6, 9, 10, 7, 4, 5, 14}
A. 3
B. 4
C. 5
D. 6
E. 7
A = {2, 9, 2, 6, 9, 10, 7, 4, 5, 14}
A. 3
B. 4
C. 5
D. 6
E. 7
17 Mar 2025, 00:56
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Bunuel
To find how many elements of list A are within 1 unit of standard deviation of the mean, we can follow these steps:
- Identify the mean and standard deviation:
Given:- Mean μ = 6.8
- Standard deviation σ = 3.6
- Mean μ = 6.8
- Define the range within 1 standard deviation:
The range within 1 standard deviation of the mean is:
μ−σ≤x≤μ+σ
Substituting the values, we get 6.8−3.6 ≤ x ≤ 6.8+3.63.2 ≤ x ≤ 10.4 - Check how many elements in A are within this range:
A={2,9,2,6,9,10,7,4,5,14} We now check each element to see if it falls within the range [3.2,10.4]
[3.2,10.4].- 2: Not within the range.
- 9: Within the range.
- 2: Not within the range.
- 6: Within the range.
- 9: Within the range.
- 10: Within the range.
- 7: Within the range.
- 4: Within the range.
- 5: Within the range.
- 14: Not within the range.
- Count the elements within the range:
The elements within the range [3.2,10.4] are 9,6,9,10,7,4,5, which makes 7 elements.
17 Mar 2025, 01:01
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Bunuel
Values within 1 SD are values that are
Greater than or equal to M-1*SD = 6.8-3.6 = 3.2 and
Less than or equal to M+1*SD = 6.8 + 3.6 = 10.4
The values that satisfy are A = {2, 9, 2, 6, 9, 10, 7, 4, 5, 14}i.e. 7 values
Answer: Option E
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