Chapter 6.2, Problem 4P

Solution

To explain: The effect of taking 14 adults on histogram and most likely number of adults.

Given information:

  $\begin{array}{c}\text{Percentage of adults that consider themselves sports fan}\left(p\right)=0.62\\ \text{Number of adults}\left(n\right)=10\\ \text{New number of adults}\left(n_1\right)=14\end{array}$

Graph:

The histogram for $n=10,p=0.62$

could be constructed as:

  

The histogram for $n=14,p=0.62$

could be constructed as:

  

Calculation:

The most likely number of adults for $n=10,p=0.62$ could be calculated as:

  $\begin{array}{c}\mu =n\times p\\ =10\times 0.62\\ =6.2\end{array}$

The most likely number of adults for $n=14,p=0.62$ could be calculated as:

  $\begin{array}{c}\mu =n\times p\\ =14\times 0.62\\ =8.680\end{array}$

From above calculation and figures, it is clear that with the increase in number of adults, the most likely number of adults has increased and the histogram has become right skewed.