Chapter 12, Problem 21PT

To determine

To Calculate :Probability of at least 10 successes using binomial distribution

Answer to Problem 21PT

  ${\displaystyle \sum _{r=10}^{15}{}^{\text{15}}{C}_r{(0.65)}^r{(0.35)}^{15-r}}$

Explanation of Solution

Given information :

We know that, for a binomial distribution, $\text{n}\text{ = 15, }\text{p}\text{ = 0}\text{.65, }q\text{ = 0}\text{.35}\text{.}$

Formula Used:

  $\text{P}\text{(}\text{r}\text{)}={}^{\text{n}}{C}_r{p}^r{q}^{n-r}$

Calculation:

  $\begin{array}{l}P(x\ge 10)=P(10)+P(11)+\mathrm{.......}+P(15)\\ $ ={}^{15}{C}_{10}{(0.65)}^{10}{(0.35)}^5+{}^{15}{C}_{11}{(0.65)}^{11}{(0.35)}^4+\mathrm{...........}$$ \mathrm{..........}+{}^{15}{C}_{15}{(0.65)}^{15}$={\displaystyle \sum _{r=10}^{15}{}^{15}{C}_r{(0.65)}^r{(0.35)}^{15-r}}\end{array}$