Question

Millionaires.Dr. Thomas Stanley of Georgia State Uni-versityhas collected information on millionaires, including theirages, since 1973. A sample of $36$millionaires has a mean age of $58.5$years and a standard deviation of $13.4$years.

a.Complete the following graph.

b.Fill in the blanks: Almost all the $36$ millionaires are between ____and____years old.

Short answer

Part(a) Required graph is given below.

Part(b) Almost all the millionaires are between $18.3$and $98.7$ years old.

Step-by-step solution

Part(a) Step 1 : Given information

We are given age sample of millionaires.

Part(a) Step 2 : Simplify

Given that $\overline{x}=58.5$

$s=13.4$

Now,

$$\begin{gathered} \overline{x}-2s=31.7 \\ \overline{x}-s=45.1 \\ \overline{x}+s=71.9 \\ \overline{x}+3s=98.7 \end{gathered}$$

Required graph is

Part(b) Step 1 : Given information

We are given age sample of millionaires.

Part(b) Step 2 : Simplify

For almost all the millionaires , age must be in between $\overline{x}-3s$and $\overline{x}+3s$according to Chebyshev's and Empirial rule.

Therefore,

$\overline{x}-3s=18.3$(given)

$\overline{x}+3s=58.5+3\left(13.4\right)=98.7$

Therefore almost all the millionaires are between $18.3$and $98.7$ years old.