7. which value is the best estimate for the standard deviation of the normal distribution shown in the…

7. 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

7. 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

Answer

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