Question

T2.2. For the Normal distribution shown, the standard deviation is closest to

(a) 0

(b) 1

(c) 2

(d) 4

(e) 5

Short answer

Option (d) 4

Step-by-step solution

Concept Introduction (Part a)

Standard deviation describes how far values vary from the mean of the set, while a high standard deviation indicates a more wide-ranging variation. A low standard deviation indicates closeness to the mean, while a high standard deviation indicates the values are spread out over a larger range.

Explanation 

We observe that the normal distribution peak is at about 4. This means that the mean is at the peak of the normal distribution.

$\mu \approx 4$

This distance from $\mu =4$to inflection point (where the curve appears approximately straight) is the standard deviation of the normal distribution.

Therefore, the standard deviation in this case is 4 (i.e.). In this case, the distance is about 4 and the standard deviation is approximately 4.