Chapter 13.4, Problem 17PPS

a.

To determine

Find the probability of through a strike in each box.

Answer to Problem 17PPS

  $0.167$

Explanation of Solution

Given information:

A baseball pitcher wants to track area where pitches have a higher probability of reaching.he divide the strike zone into six boxes.

  

Calculation:

The strike are having six boxes of equal size, and strike equally hit each box so the probability will be $\frac{1}{6}=0.167$ .

Hence, the probability of through a strike in each box is $0.167$ .

b.

To determine

Design a simulation to estimate the probability of through a strike in each box.

Answer to Problem 17PPS

  $0.20,0.15,0.12,0.21,0.18,0.14$

Explanation of Solution

Given information:

A baseball pitcher wants to track area where pitches have a higher probability of reaching.he divide the strike zone into six boxes.

  

Calculation:

To simulate the strike in the square, use a die to generate integers. Each side represents a square. Run $100$ trial of strike ( $100$ random numbers) and record the frequency of observed outcome.

  $\begin{array}{cccccccc}outcome\left(square\right)& 1& 2& 3& 4& 5& 6& total\\ frequency& 20& 15& 12& 21& 18& 14& 100\end{array}$

Divide each frequency by total frequency,

  $\begin{array}{cccccccc}outcome\left(square\right)& 1& 2& 3& 4& 5& 6& total\\ frequency& 20& 15& 12& 21& 18& 14& 100\\ probability& \begin{array}{l}20/100\\ =0.20\end{array}& \begin{array}{l}15/100\\ =0.15\end{array}& \begin{array}{l}12/100\\ =0.12\end{array}& \begin{array}{l}21/100\\ =0.21\end{array}& \begin{array}{l}18/100\\ =0.18\end{array}& \begin{array}{l}14/100\\ =0.14\end{array}& \begin{array}{l}100/100\\ =1\end{array}\end{array}$

Hence, the probability strike land in each square is, $0.20,0.15,0.12,0.21,0.18,0.14$

c.

To determine

Compare the values of part $\left(a\right)\&\left(b\right)$ .

Answer to Problem 17PPS

Most of the value are close to $0.167$ .

Explanation of Solution

Given information:

A baseball pitcher wants to track area where pitches have a higher probability of reaching.he divide the strike zone into six boxes.

  

Calculation:

The probability of through a strike in each box is $0.167$ and $0.20,0.15,0.12,0.21,0.18,0.14$

Most of the value are close to $0.167$ .