Chapter 6.2, Problem 2MRPS

Solution

(a)

To construct: The histogram for the provided binomial distribution.

Given information:

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

Graph:

The histogram is constructed as:

  

(b)

To find: The number of adults that consider themselves sports fan.

The number of adults is 8.680.

Calculation:

The number of people could be calculated as:

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

The required number is 8.680.

(c)

To find: The probability that at least 7 adults are considering themselves a sports fan.

The probability is 0.8838.

Calculation:

Consider, X be the random variable that shows the number of US adults that consider themselves a fan.

The probability is calculated as:

  $\begin{array}{c}P\left(X\ge 7\right)=P\left(X=7\right)+P\left(X=8\right)+\mathrm{........}+P\left(X=14\right)\\ {=}^{14}{C}_7{\left(0.62\right)}^7\times {\left(1-0.62\right)}^{14-7}{+}^{14}{C}_8{\left(0.62\right)}^8\times {\left(1-0.62\right)}^{14-8}+\mathrm{.....}{+}^{14}{C}_{14}{\left(0.62\right)}^{14}\times {\left(1-0.62\right)}^{14-14}\\ =0.13828+0.19742+\mathrm{.......}+0.00124\\ =0.8838\end{array}$

The required probability is 0.8838.