POTUS The accompanying graph is a histogram of ages of U.S. presidents at the time they were inaugurated (from Data Set 12).

a. Identify two features of the vertical scale that cause the graph to be somewhat misleading.

b. Does the histogram appear to show data from a population having a normal distribution? Explain.

c. From the graph, identify the lowest and highest possible ages, then use the range rule of thumb to estimate the standard deviation of the ages. How does the result compare to the standard deviation of 6.6 years calculated from the original list of sample values?

Problem 4CRE

Answer:

Step1 of 3:

We have The accompanying graph is a histogram of ages of U.S. presidents at the time they were inaugurated (from Data Set 12).

Step2 of 3:

a. Identify two features of the vertical scale that cause the graph to be somewhat misleading.

b. Does the histogram appear to show data from a population having a normal distribution? Explain.

c. From the graph, identify the lowest and highest possible ages, then use the range rule of thumb to estimate the standard deviation of the ages. How does the result compare to the standard deviation of 6.6 years calculated from the original list of sample values?

Step3 of 3:

a).

The vertical scale does not start at 0, so differences are somewhat distorted. By using a scale ranging from 1 to 29 for frequencies that range 2 to 14, the graph is flattened, so differences are not shown as they should be.

b).

The graph depicts a distribution that is not exactly normal, but it is approximately normal because it is roughly bell shaped.

c).

In a above given histogram we have,

Minimum value = 42years

Maximum value = 70years

Using the range rule of thumb, the standard deviation is estimated to be = 7 years. The estimate of 7 years is very close to the actual standard deviation of 6.6 years, so the range rule of thumb works quite well here.