Chapter 12.7, Problem 23PPS

To determine

Find the probability at least $146$ of teens surveyed watch at least one reality show.

Answer to Problem 23PPS

  $0.8238$

Explanation of Solution

Given information:

According to an online poll $70\%$ of teens watch at least one reality show. Dillon surveyed $200$ random teens.

Calculation:

Standard deviation,

  $\begin{array}{l}\sigma =\sqrt{nsf}\\ =\sqrt{200\times 0.70\times 0.30}\\ =6.48\\ Thez-scoreforx=146is\\ z=\frac{\mu -x}{\sigma }\\ =\frac{140-146}{6.48}\\ =-0.93\end{array}$

The probability at least $146$ of teens surveyed watch at least one reality show,

  $\begin{array}{l}P\left(X\ge 146\right)=1-P\left(X\le 145\right)\\ =1-P\left(z\le -0.93\right)\\ =1-0.1762\\ =0.8238\end{array}$

Hence, the probability is $0.8238$ .