The distribution of seed pod diameters of a particular tree is normal (bell-curve-shaped), with a mean of 3 inches and a standard deviation of 0.25 inches. Which is the closest proportion of seed pods that have a diameter between 2.75 inches and 3.25 inches?

A. 1/4
B. 1/3
C. 1/2
D. 2/3
E. 3/4

The correct answer is (D). The values 2.75 and 3.25 were obtained by subtracting one standard deviation from the mean of 3 to get 2.75 inches, and adding one standard deviation to it to get 3.25. A normal distribution has about 68 % of its data within one standard deviation of the mean. Of the answer choices, 2/3 is the closest value to 68%, and thus the answer is D.
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This answer is not at all clear. Could you explain it better, please?

I will really appreciate it.

First of all note:
68% is 0.68
2/3 is 0.66… ≈ 0.67

Secondly, you should review the facts about normal distribution.

This is the fact we use here:
A normal distribution has about 68% of its data within one standard deviation of the mean.

Here is the diagram, which shows how the mean (3.00 inches) and the values 2.75 inch, 3.25 inch relate according to the 68%-rule.



Each point represents the number of seed pods of a certain diameter.

The mean value is:
(diameter1 × number1 + diameter2 × number2 + … + diameterN × numberN) / (number1 + number2 + … + numberN)

The grey points represent all seed pods that have their diameters between 2.75 and 3.25. There are (numberK + … + numberM) of those seed pods.

The theorem says that (numberK + … + numberM)/(number1 + … + numberN) is about 68%.