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Problem 10

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

Expert verified

The probability of at most three successes in five independent Bernoulli trials with \(p=0.1\) and \(q=0.9\) is approximately 0.99954.

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Chapter 8

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

Chapter 8

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Chapter 8

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 .

Chapter 8

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

Chapter 8

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?

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