Chapter 18, Problem 9E

To determine

To explain what do you think of this claim.

Explanation of Solution

It is given in the question, the professor in the class has each person toss a coin $25$ times and calculate the proportion of his or her tosses that were heads. And the results of the students are plotted by a histogram by the professor of these several proportions. Since we know that the probabilities of the toss to be head and to be tail is equal in proportions as half. And in that one of the students in the class claims to have tossed her coin $200$ times and found only $42\%$ heads. Thus, the sample mean and the standard deviation for this will be:

  $\begin{array}{l}\mu =p=0.5\\ \sigma =\sqrt{\frac{pq}{n}}\\ =\sqrt{\frac{0.5(0.5)}{200}}\\ =0.0354\end{array}$

Then the z -score will be as:

  $\begin{array}{l}z=\frac{0.42-0.5}{0.0354}\\ =-2.26\end{array}$

So, we can say that the student’s sample proportion is about $2.26$ standard deviations below the expected proportion which although unusual is not appropriate.