In Exercises \(1-10,\) you are performing five independent Bernoulli trials with \(p=.1\) and \(q=.9 .\) Calculate the probability of the stated outcome. Check your answer using technology. [HINT: See Quick Example \(8 .\) At most three successes

What do you expect to happen to the probabilities in a probability distribution as you make the measurement classes smaller?

In a certain set of five scores, there are as many values above the mean as below it. It follows that (A) The median and mean are equal. (B) The mean and mode are equal. (C) The mode and median are equal. (D) The mean, mode, and median are all equal.

LSAT Scores LSAT test scores are normally distributed with a mean of 151 and a standard deviation of 7 . Find the probability that a randomly chosen test- taker will score between 137 and 158 .

Explain how you can use a sample to estimate an expected value.

Are based on the following table, which shows crashworthiness ratings for several categories of motor vehicles. \({ }^{10}\) In all of these exercises, take \(X\) as the crash-test rating of a small car, \(Y\) as the crash-test rating for a small SUV, and so on, as shown in the table. $$\begin{array}{|r|c|c|c|c|c|}\hline & & {}{} {\text { Overall Frontal Crash Test Rating }} \\\\\hline &\begin{array}{c}\text { Number } \\\\\text { Tested }\end{array} & \begin{array}{c}3 \\\\(\text { Good })\end{array} & \begin{array}{c}2 \\\\\text { (Acceptable) }\end{array} & \begin{array}{c}1 \\\\\text {(Marginal) }\end{array} & \begin{array}{c}0 \\\\\text { (Poor) }\end{array} \\\\\hline \text { Small Cars, } X &16 & 1 & 11 & 2 & 2 \\\\\hline \text { Small SUVs, } Y & 10 & 1 & 4 & 4 & 1 \\\\\hline \text { MediumSUVs,} Z & 15 & 3 & 5 & 3 & 4 \\\\\hline \text { Passenger Vans, } U & 13 & 3 & 0 & 3 & 7 \\\\\hline \text { Midsize Cars, } V & 15 & 3 & 5 & 0 & 7 \\\\\hline \text { Large Cars, } W & 19 & 9 & 5 & 3&2 \\\\\hline\end{array}$$ Which of the six categories shown has the lowest probability of a Good rating?