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.) $$ \begin{array}{|c|c|c|c|c|} \hline x & 1 & 2 & 3 & 4 \\ \hline \boldsymbol{P}(\boldsymbol{X}=\boldsymbol{x}) & .1 & .2 & .5 & .2 \\ \hline \end{array} $$

What percentage of U.S. families earned an after-tax income of \(\$ 80,000\) or more?

Your pet tarantula, Spider, has a .12 probability of biting an acquaintance who comes into contact with him. Next week, you will be entertaining 20 friends (all of whom will come into contact with Spider). a. How many guests should you expect Spider to bite? b. At your last party, Spider bit 6 of your guests. Assuming that Spider bit the expected number of guests, how many guests did you have?

The following table shows tow ratings (in pounds) for some popular sports utility vehicles in \(2000:^{6}\) $$ \begin{array}{|l|c|} \hline \text { Vehicle } & \text { Tow Rating } \\ \hline \text { Mercedes Grand Marquis V8 } & 2,000 \\ \hline \text { Jeep Wrangler I6 } & 2,000 \\ \hline \text { Ford Explorer V6 } & 3,000 \\ \hline \text { Dodge Dakota V6 } & 4,000 \\ \hline \text { Mitsubishi Montero V6 } & 5,000 \\ \hline \text { Ford Explorer V8 } & 6,000 \\ \hline \text { Dodge Durango V8 } & 6,000 \\ \hline \text { Dodge Ram 1500 V8 } & 8,000 \\ \hline \text { Ford Expedition V8 } & 8,000 \\ \hline \text { Hummer 2-Door Hardtop } & 8,000 \\ \hline \end{array} $$ Let \(X\) be the tow rating of a randomly chosen popular SUV from the list above. a. What are the values of \(X\) ? b. Compute the frequency and probability distributions of \(X .\) [HINT: See Example \(5 .]\) c. What is the probability that an SUV (from the list above) is rated to tow no more than 5,000 pounds?

\- Find an algebraic formula for the population standard deviation of a sample \(\\{x, y\\}\) of two scores \((x \leq y)\).

You are a manager in a precision manufacturing firm and you must evaluate the performance of two employees. You do so by examining the quality of the parts they produce. One particular item should be \(50.0 \pm 0.3 \mathrm{~mm}\) long to be usable. The first employee produces parts that are an average of $50.1 \mathrm{~mm}\( long with a standard deviation of \)0.15 \mathrm{~mm}$. The second employee produces parts that are an average of \(50.0 \mathrm{~mm}\) long with a standard deviation of \(0.4 \mathrm{~mm}\). Which employee do you rate higher? Why? (Assume that the empirical rule applies.)