Question

1. which value is the best estimate for the standard deviation of the normal distribution shown in the figure? mean = 28 min = 21 max = 35 a) 1 b) 2 c) 5 d) 12 e) 28

Explanation:

Step1: Recall range - rule - of - thumb

The range - rule - of - thumb for a normal distribution is that the range (Max - Min) is approximately 4 to 6 times the standard deviation $\sigma$. The formula is $\text{Range}=\text{Max}-\text{Min}\approx4\sigma$ to $6\sigma$.

Step2: Calculate the range

Given $\text{Max} = 35$ and $\text{Min}=21$, the range is $\text{Range}=35 - 21=14$.

Step3: Estimate the standard deviation

Using the range - rule - of - thumb $\text{Range}\approx4\sigma$ to $6\sigma$. If we use $\text{Range}\approx6\sigma$, then $\sigma=\frac{\text{Range}}{6}$. Substituting the range value, we get $\sigma=\frac{14}{6}\approx2.33$. If we use $\text{Range}\approx4\sigma$, then $\sigma=\frac{\text{Range}}{4}=\frac{14}{4} = 3.5$. A good estimate is closer to 2.

Answer:

B. 2