Chapter 17, Problem 42E

To determine

To Explain: the archer proceeds to shoot arrows, ending up with 45 bull's-eyes in 50 rounds, and is now persuaded that the new bow is stronger.

Answer to Problem 42E

0.0295

Explanation of Solution

Given:

  $\begin{array}{c}p=0.80\\ n=50\end{array}$

Formula used:

  $P\left(X=r\right)=C{}_r{\left(p\right)}^r{\left(1-p\right)}^{n-r}$

Calculation:

Required probability is

  $\begin{array}{c}P\left(X=45\right)=C{}_{45}{\left(0.8\right)}^{45}{\left(0.2\right)}^5\\ =2118760\left(0.00004356\right)\left(0.00032\right)\\ =0.0295\end{array}$

There is 2.95% possibility that researcher makes 45 out of 50 shots.

The new bow is not better because the chance is too limited.