Problem Solving

Roland2rule wrote:The arithmetic mean and standard deviation of a certain normal distribution are 13.5 and 1.5, respectively. What value is exactly 2 standard deviations less than the mean?

A. 10.5
B. 11
C. 11.5
D. 12
E. 12.5

------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.
------ONTO THE QUESTION!!!-----------------------------------

The arithmetic mean and standard deviation of a certain normal distribution are 13.5 and 1.5, respectively. What value is exactly 2 standard deviations less than the mean?
2 standard deviations BELOW the mean = 13.5 - (2)(1.5)
= 13.5 - 3
= 10.5
= A

Cheers,
Brent

BTGmoderatorRO wrote:The arithmetic mean and standard deviation of a certain normal distribution are 13.5 and 1.5, respectively. What value is exactly 2 standard deviations less than the mean?

A. 10.5
B. 11
C. 11.5
D. 12
E. 12.5

OA is A

I would an expert to give the mathematical approach to the question. Thanks for your time.

Two standard deviations less than the mean is 13.5 - 2 x 1.5 = 13.5 - 3 =10.5.

Answer: A