Q. 20 - Elementary Statistics

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.

Step-by-Step Solution

Answer

Part(a) Required graph is given below.

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

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.