In a certain experiment, the data collected is the number of organisms per sample, and this data follows a normal distribution. If the sample of data has a mean of 60 and a standard deviation of 12, which of the following is exactly 1.75 standard deviations more than the mean?

A)48
B)60
C)72
D)77.5
E)81

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.

---------------------------------
Now the original question...
So, 1.75 standard deviations more than the mean = 60 + (1.75)(12)
= 60 + 21
= 81
= E

Cheers,
Brent

swerve wrote:In a certain experiment, the data collected is the number of organisms per sample, and this data follows a normal distribution. If the sample of data has a mean of 60 and a standard deviation of 12, which of the following is exactly 1.75 standard deviations more than the mean?

A. 48
B. 60
C. 72
D. 77.5
E. 81

The OA is E

Source: Manhattan Prep

The value that is exactly 1.75 standard deviations more than the mean is:

60 + 1.75 x 12 = 60 + 21 = 81

Answer: E