Chapter 6.3, Problem 79E

(a)

To determine

To calculate;the value of $P(X=17)$

Answer to Problem 79E

  $\text{P(X = 17) =}24.28\%$

Explanation of Solution

Given;

  $\begin{array}{l}n=20\\ p=0.85\end{array}$

Explanation;

  $\begin{array}{l}\text{Definition Binomial Probability:}\\ $ \text{P(X = k) = }\left(\begin{array}{l}n\\ k\end{array}\right)\times p^k\times {(1-p)}^{n-k}$\end{array}$

  $\text{P(X = 17) = }\left(\begin{array}{l}20\\ 17\end{array}\right)\times {(0.85)}^{17}\times {(0.15)}^{20-17}\approx 0.2428=24.28\%$

(b)

To determine

To calculate;the value of $P(X\le 12)$

Answer to Problem 79E

Yes. $\text{P(X }\le \text{ 12)}\approx 0.59\%$

Explanation of Solution

Given;

  $\begin{array}{l}n=20\\ p=0.85\end{array}$

Explanation;

  $\begin{array}{l}\text{Definition Binomial Probability:}\\ $ \text{P(X = k) = }\left(\begin{array}{l}n\\ k\end{array}\right)\times p^k\times {(1-p)}^{n-k}$\end{array}$

  $\text{P(X }\le \text{ 12) = P(X = 0) + P(X = 1) + }\mathrm{...}\text{ + P(X = 12)}\approx 0.0059\approx 0.59\%$

As the probability is a really small value, therefore the event is unlikely to happen by chance and therefore Judy must be suspicious.