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Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: In a population of chickens, the average (arithmetic mean)
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06 Nov 2019, 12:47
06 Nov 2019, 12:47
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In a population of chickens, the average (arithmetic mean) weight is 6.3 pounds, and the standard deviation is 1.2 pounds. Which of the following weights (in pounds) are within 1.5 units of the standard deviation of the mean?
Indicate all weights.
A. 4.4
B. 4.6
C. 5.1
D. 5.2
E. 6.9
F. 7.6
G. 7.7
H. 8.2
Indicate all weights.
A. 4.4
B. 4.6
C. 5.1
D. 5.2
E. 6.9
F. 7.6
G. 7.7
H. 8.2
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Official Answer
B,C,D,E,F,G
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: In a population of chickens, the average (arithmetic mean)
[#permalink]
26 Jan 2020, 09:18
26 Jan 2020, 09:18
1
----ASIDE---------------------
A little extra background on standard deviations above and below the mean
If, for example, a set has a standard deviation of 4, then:
1 standard deviation = 4
2 standard deviations = 8
3 standard deviations = 12
1.5 standard deviations = 6
0.25 standard deviations = 1
etc
So, if the mean of a set is 9, and the standard deviation is 4, then:
2 standard deviations ABOVE the mean = 17 [since 9 + 2(4) = 17]
1.5 standard deviations BELOW the mean = 3 [since 9 - 1.5(4) = 3]
3 standard deviations ABOVE the mean = 21 [since 9 + 3(4) = 21]
etc.
-------------------------------
In a population of chickens, the average (arithmetic mean) weight is 6.3 pounds, and the standard deviation is 1.2 pounds. Which of the following weights (in pounds) are within 1.5 units of the standard deviation of the mean?
1.5 units of standard deviation ABOVE the mean = 6.3 + (1.5)(1.2) = 8.1
1.5 units of standard deviation BELOW the mean = 6.3 - (1.5)(1.2) = 4.5
So, the weights that are WITHIN 1.5 units of the standard deviation of the mean will be BETWEEN 4.5 and 8.1
Answer: B, C, D, E, F, G
Cheers,
Brent
A little extra background on standard deviations above and below the mean
If, for example, a set has a standard deviation of 4, then:
1 standard deviation = 4
2 standard deviations = 8
3 standard deviations = 12
1.5 standard deviations = 6
0.25 standard deviations = 1
etc
So, if the mean of a set is 9, and the standard deviation is 4, then:
2 standard deviations ABOVE the mean = 17 [since 9 + 2(4) = 17]
1.5 standard deviations BELOW the mean = 3 [since 9 - 1.5(4) = 3]
3 standard deviations ABOVE the mean = 21 [since 9 + 3(4) = 21]
etc.
-------------------------------
In a population of chickens, the average (arithmetic mean) weight is 6.3 pounds, and the standard deviation is 1.2 pounds. Which of the following weights (in pounds) are within 1.5 units of the standard deviation of the mean?
1.5 units of standard deviation ABOVE the mean = 6.3 + (1.5)(1.2) = 8.1
1.5 units of standard deviation BELOW the mean = 6.3 - (1.5)(1.2) = 4.5
So, the weights that are WITHIN 1.5 units of the standard deviation of the mean will be BETWEEN 4.5 and 8.1
Answer: B, C, D, E, F, G
Cheers,
Brent
Re: In a population of chickens, the average (arithmetic mean)
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16 Jan 2022, 04:22
16 Jan 2022, 04:22
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