Chapter 6.2, Problem 38E

To determine

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

Explanation of Solution

Given:

  $\begin{array}{c}{\mu }_G=560\\ {\sigma }_G=185\end{array}$

Shape:

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

Center:

Subtracting the constant to every data value, then the center of the distribution is also decreased by that constant value thus P is a normal distribution function.

  $\begin{array}{c}{\mu }_P={\mu }_G-65\\ =560-65\\ =495\end{array}$

Spread:

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

  ${\sigma }_P={\sigma }_G=185$

So P is a normal distribution with mean=$495 and standard deviation=$185