Bunuel wrote:

500 records have a distribution that is symmetric about the mean 10. If 68 percent of the distribution lies within one standard deviation of the mean, and the deviation is 2, then at least how many of the records are less than 12?

(A) 160

(B) 320

(C) 340

(D) 420

(E) 460

Attachment:

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If the normal distribution is familiar, finding the answer should be quick.

1. Normal distribution

It is a normal distribution because 68 percent of the distribution lies within one standard deviation of the mean.

--- Half of that 68% lies to the right of mean (diagram: +1 SD on right and -1 SD on left)

--- Half of 68% for +1 SD is 34%. (mean 50% + 34%) = 84%

2) Value of 12 corresponds with 84% of distribution

Mean is 10, SD is 2: 12 is 10 (mean) + 2 (1 SD) which is equivalent to 84 percent of the distribution (on diagram, horizontal lines' vertical marks correspond)

3) At least how many of the records are less than 12?

Less than 12 = 34% + 34% + 14% + 2% (all intervals, 84 to 0, see shaded areas) = 84%

4) 500 records, 84 percent of which are less than 12: .84 * 500 = 420

Answer (D)

_________________

In the depths of winter, I finally learned

that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"