Chapter 11.2, Problem 20E

(a)

To determine

To explain:

The conclusion for following statement using histogram:

  $17$ heads observed on flipping a coin for $50$ times

Answer to Problem 20E

The company claims about $17$ heads is incorrect as the probability value for the event is not close enough to the mean of the histogram.

Explanation of Solution

Given information:

  

  $\begin{array}{l}n\left(E\right)=17\\ n\left(S\right)=50\end{array}$

Formula used:

Probability of an event is given by the following expression:

  $P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}$

Where,

  $n\left(E\right)$ : Number of ways it can happen

  $n\left(S\right)$ : Total number of outcomes

Calculation:

On flipping a coin for $50$ times, $17$ heads observed. Now, probability of getting $17$ heads is calculated as below:

  $\begin{array}{l}P\left(17\right)=\frac{17}{50}\\ P\left(17\right)=0.34\end{array}$

Here, $P\left(17\right)=0.34$ is not enough close to the mean of the histogram $0.50$ . So, the company claims about $17$ heads is false.

(b)

To determine

To explain:

The conclusion for following statement using histogram:

  $23$ heads observed on flipping a coin for $50$ times

Answer to Problem 20E

The company claims about $23$ heads is correct as the probability value for the event is close enough to the mean of the histogram.

Explanation of Solution

Given information:

  

  $\begin{array}{l}n\left(E\right)=23\\ n\left(S\right)=50\end{array}$

Formula used:

Probability of an event is given by the following expression:

  $P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}$

Where,

  $n\left(E\right)$ : Number of ways it can happen

  $n\left(S\right)$ : Total number of outcomes

Calculation:

On flipping a coin for $50$ times, $23$ heads observed. Now, probability of getting $23$ heads is calculated as below:

  $\begin{array}{l}P\left(23\right)=\frac{23}{50}\\ P\left(23\right)=0.46\end{array}$

Here, $P\left(23\right)=0.46$ is close to the mean of the histogram $0.50$ . So, the company claims about $23$ heads is true.