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14 Sep 2013, 20:38
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B
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33%
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A researcher investigating mosquito populations recorded a list of estimates of mosquito populations at each of \(n\) different marshland locations in a certain country. The distribution of these estimates was symmetric about the average (arithmetic mean), and 70% of these population estimates were within one standard deviation of the mean. Of these estimates, 75 were more than one standard deviation below the mean. Approximately how many of the estimates were within one standard deviation of the mean?
A) 175
B) 350
C) 375
D) 425
E) 500
A) 175
B) 350
C) 375
D) 425
E) 500
02 Nov 2014, 21:40
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carcass
A researcher investigating mosquito populations recorded a list of estimates of mosquito populations at each of \(n\) different marshland locations in a certain country. The distribution of these estimates was symmetric about the average (arithmetic mean), and 70% of these population estimates were within one standard deviation of the mean. Of these estimates, 75 were more than one standard deviation below the mean. Approximately how many of the estimates were within one standard deviation of the mean?
A) 175
B) 350
C) 375
D) 425
E) 500
A) 175
B) 350
C) 375
D) 425
E) 500
Let M = Arithematic Mean
70% Population Estimate is within 1 Standard Deviation of Mean (1D)
Let this 70% = X
i.e. (M-1D) <= X <= (M+1D)
70% of estimate is within 1 SD of Mean, it implies that 30% of estimates lie in the region on the left side of (M-1D) and on the right side of (M+1D).
Since, the estimates are Symmetric around the mean,
15% of Estimate is on left side of (M-1D), and
15% of Estimate is on right side of (M+1D).
Given, 15% of Estimate on left side of (M-1D) = 75
Therefore, X can be determined by:
15/70 = 75/X
X = 350
Hence, Answer is B
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14 Sep 2013, 23:53
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carcass
A researcher investigating mosquito populations recorded a list of estimates of mosquito populations at each of \(n\) different marshland locations in a certain country. The distribution of these estimates was symmetric about the average (arithmetic mean), and 70% of these population estimates were within one standard deviation of the mean. Of these estimates, 75 were more than one standard deviation below the mean. Approximately how many of the estimates were within one standard deviation of the mean?
A) 175
B) 350
C) 375
D) 425
E) 500
A) 175
B) 350
C) 375
D) 425
E) 500
If 70% of population is within 1 standard deviation mean then 30% are more than 1 standard deviation below the mean.
Taking symmetric about the mean,
75 are more than 1 sd below the mean therefore these 75 constitute 15% (Taking 15% below the mean and 15% above the mean)
Therefore total population is 500.
Therefore 70% of 500 is 350. who are within 1 standard deviation from the mean.
Hence B
