Chapter 12.7, Problem 21PPS

a.

To determine

Graph the binomial probability distribution.

Answer to Problem 21PPS

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Explanation of Solution

Given information:

An online poll showed that $5\%$ of adults still play vinyl records. Moe surveyed $8$ random people from the population.

Calculation:

Table of probabilities for all possible value of $x$ .

  $\begin{array}{ccccccccc}X& 0& 1& 2& 3& 4& 5& 6& 7\\ P\left(X=x\right)& 0.66342043& 0.27933492& 0.05145643& 0.00541647& 0.00035635& 0.000015& 0.00000039& 0.00000001\end{array}$

  

Hence the graph represents the binomial probability distribution.

b.

To determine

Find the probability that no more than $2$ of the people surveyed still play vinyl records.

Answer to Problem 21PPS

  $0.9942$

Explanation of Solution

Given information:

An online poll showed that $5\%$ of adults still play vinyl records. Moe surveyed $8$ random people from the population.

Calculation:

The probability that no more than $2$ of the people surveyed still play vinyl records,

  $\begin{array}{l}P\left(X\le 2\right)={\displaystyle \sum _{x=0}^2\left(\underset{x}{\overset{8}{{\displaystyle }}}\right)}{\left(0.05\right)}^x{\left(0.95\right)}^{8-x}\\ =0.9942\end{array}$

Hence the probability is $0.9942$ .