Chapter 8: Chapter 8

Find the indicated probabilities. $$ \mu=50, \sigma=10, \text { find } P(30 \leq X \leq 62) $$

In Exercises \(11-16\), calculate the expected value of \(X\) for the given probability distribution. $$ \begin{array}{|c|c|c|c|c|} \hline x & 0 & 1 & 2 & 3 \\ \hline P(X=x) & .5 & .2 & .2 & .1 \\ \hline \end{array} $$

In exercise, \(X\) is a binomial variable with \(n=6\) and \(p=.4 .\) Compute the given probabilities. Check your answer using technology. $$ P(X=3) $$

Calculate the standard deviation of \(X\) for each probability distribution. (You calculated the expected values in the last exercise set. Round all answers to two decimal places.) $$ \begin{array}{|c|c|c|c|c|} \hline x & 2 & 4 & 6 & 8 \\ \hline P(X=x) & \frac{1}{20} & \frac{15}{20} & \frac{2}{20} & \frac{2}{20} \\ \hline \end{array} $$

Calculate the expected value of \(X\) for the given probability distribution. $$ \begin{array}{|c|c|c|c|c|} \hline \boldsymbol{x} & 1 & 2 & 3 & 4 \\ \hline \boldsymbol{P}(\boldsymbol{X}=\boldsymbol{x}) & .1 & .2 & .5 & .2 \\ \hline \end{array} $$

In exercise, \(X\) is a binomial variable with \(n=6\) and \(p=.4 .\) Compute the given probabilities. Check your answer using technology. $$ P(X=4) $$

In exercise, \(X\) is a binomial variable with \(n=6\) and \(p=.4 .\) Compute the given probabilities. Check your answer using technology. $$ P(X \leq 2) $$

\(X\) is the sum of the numbers that face up when two dice are rolled.

Calculate the standard deviation of \(X\) for each probability distribution. (You calculated the expected values in the last exercise set. Round all answers to two decimal places.)$$ \begin{array}{|c|c|c|c|c|c|c|} \hline \boldsymbol{x} & -5 & -1 & 0 & 2 & 5 & 10 \\ \hline \boldsymbol{P}(\boldsymbol{X}=\boldsymbol{x}) & .2 & .3 & .2 & .1 & .2 & 0 \\ \hline \end{array} $$

Find the indicated probabilities. $$ \mu=100, \sigma=15, \text { find } P(110 \leq X \leq 130) $$