Chapter 6.3, Problem 87E

To determine

To find: $P\left(X\le 7\right)$and interpret it.

Answer to Problem 87E

  $P\left(X\le 7\right)=0.0726$

Explanation of Solution

Given:

Number of trials ( n ) = 12

Probability of success ( p ) = 0.80

Calculation:

Consider, X be the random variable that follows the binomial distribution with parameters n = 12 and p = 0.80.

  $P\left(X\le 7\right)$can be calculated as:

  $\begin{array}{c}P\left(X\le 7\right)=P\left(X=0\right)+P\left(X=1\right)+\mathrm{....}+P\left(X=7\right)\\ ={\displaystyle \sum _{r=0}^7{}^{12}{C}_r\times {\left(0.80\right)}^r\times {\left(1-0.80\right)}^{12-r}}\\ =0.0726\end{array}$

Hence, the probability is 0.0726.

Interpretation:

There are 7.26% chances that spinner would land in the blue region at most 7 times.