Chapter 6.2, Problem 37E

To determine

To Explain: the shape, center and variability of the probability distribution function

Explanation of Solution

Given:

  $\begin{array}{l}{\mu }_X=15\\ {\sigma }_X=6.5\end{array}$

Shape:

Adding the constant to every data value will not affect the shape of the distribution and thus T is a normal distribution function.

Center:

Adding the constant to every data value, then the center of the distribution is also increased by that constant value thus T is a normal distribution function.

  $\begin{array}{c}{\mu }_T={\mu }_X+5\\ =15+5\\ =20\end{array}$

Spread:

Adding the constant to every data value, then the spread of the distribution will not affect, it remains unchanged.

  ${\sigma }_T={\sigma }_X=6.5$

So T is a normal distribution with mean=20 minutes and standard deviation=6.5 minutes