You're going to have to work out the z-scores of both values in each option and see if it makes sense.

n = m + sz

The mean is 20 and the standard deviation is 3.

So let's find try the z-scores of the outer range values and determine their probabilities:

from 14-20:

n = m + sz
20 = 20 + 3z and 14 = 20 + 3z
0 = 3z and -6 = 3z
z = 0 and z = -2

So now using a z-score table, such as the one below, find the probabilities.

z = 0 is easy, it's 0.5
z = -2 is 0.02275

Subtract the smaller from the larger to get the probability of getting in the range:

0.5 - 0.02275 = 0.47725 (so times 1000, you get 477.25, which is not about 340, so this option is wrong)
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Now trying option 2, from 17-29:

n = m + sz
29 = 20 + 3z and 17 = 20 + 3z
9 = 3z and -3 = 3z
z = 3 and z = -1

0.99865 - 0.158655 = 0.839995 (not 680, so not the answer)
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Now trying option 3, from 20-23:

n = m + sz
23 = 20 + 3z and 20 = 20 + 3z
3 = 3z and 0 = 3z
z = 1 and z = 0

0.841345 - 0.5 = 0.341345 (close to 340, so is your answer)

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2 years ago