Chapter 6.3, Problem 97E

(a)

To determine

To calculate; the value of $P(X=3)$

Answer to Problem 97E

  $\text{P(X = 3)}=12.8\%$

Explanation of Solution

Given;

  $p=0.20$

Explanation;

  $\begin{array}{l}\text{Definition Geometric Probability:}\\ $ {\text{P(X = k) = q}}^{k-1}\times p={(1-p)}^{k-1}p$\end{array}$

  ${\text{P(X = 3) = (1 - 20)}}^{\text{3 - 1}}(0.20)=0.128=12.8\%$

(b)

To determine

To calculate; the value of $P(X>10)$

Answer to Problem 97E

  $\text{P(X > 10)}=10.74\%$

Explanation of Solution

Given;

  $p=0.20$

Explanation;

  $\begin{array}{l}\text{Definition Geometric Probability:}\\ $ {\text{P(X = k) = q}}^{k-1}\times p={(1-p)}^{k-1}p$\end{array}$

  $\begin{array}{l}\text{P(X > 10) = 1 - P(X }\le \text{10) = 1 - P(X = 1) - P(X = 2) - }\mathrm{...}\text{ - P(X = 10)}\\ =1-0.8926=0.1074=10.74\%\end{array}$