Chapter 10.1, Problem 4E

(a)

To determine

To Calculate: the probability

Answer to Problem 4E

  $\text{P}\left(z<-2.61\right)=0.00453$

Explanation of Solution

Given:

From previous exercise

  $\begin{array}{c}\mu =0.40\\ \sigma =0.07745\\ {\widehat{p}}_G-{\widehat{p}}_D=0.20\end{array}$

Formula used:

  $z=\frac{x-\mu }{\sigma }$

Calculation:

  $\begin{array}{c}z=\frac{x-\mu }{\sigma }\\ =\frac{0.20-0.40}{0.07745}\\ \approx -2.61\end{array}$

  

  $\begin{array}{c}\text{P}\left(z<-2.61\right)=0.00453\\ =0.45\%\end{array}$

(b)

To determine

To Explain: the reason of company’s claim about doubt

Explanation of Solution

Since the probability is $\text{P}\left(z<-2.61\right)=0.00453$ which is very small, this would gives the reason to doubt the company’s claim