Chapter 2, Problem 7PT

To determine

To select: the best answer for the given question.

Answer to Problem 7PT

Option (c) is right option.

Explanation of Solution

Given:

97% have heights between 5’0” and 7’0”.

Calculation:

According to the $68-95-99.7$ rule, note that $99.7\%$ of the observation lies within threestandard deviations of the mean $(\mu \pm 3\sigma )$

Thus,

  $\begin{array}{l}\mu -3\sigma =5^{\prime }\hfill \\ \mu +3\sigma =7^{\prime }\hfill \end{array}$

Using equations (1) and (2), obtain the value of standard deviation as follows.

As per the requirement, subtract (1) from (2).

  $\begin{array}{l}(2)-(1)\hfill \\ \Rightarrow (\mu +3\sigma )-(\mu -3\sigma )=7-5^{*}\hfill \\ \Rightarrow 6\sigma =2^{\prime }\hfill \\ \Rightarrow \sigma =\frac{2}{6}\hfill \\ ={0.3333}^{\prime }\hfill \end{array}$

It is known that 12 inches $\left({12}^{*}\right)$ constitutes 1 foot $\left(1^{\prime }\right)$

Thus the standard deviation is obtained as

  $\sigma =0.3333\times 12"=4"$

Option (c) is right option.

Conclusion:

Therefore option (c) is right option.