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Analyzing Binomial Probability in Automobile Accidents and Stolen Car Recoveries

This guide explores binomial probability through two scenarios: automobile accidents attributed to driver fatigue and the recovery of stolen cars. We first examine the likelihood of exactly three out of six surveyed individuals experiencing accidents due to fatigue, given a claimed 10% rate. Next, we analyze the probability of recovering exactly four out of five stolen cars, considering a 63% recovery rate. The text also includes directions for constructing histograms for visual representation of these binomial distributions, making statistical concepts more accessible and understandable.

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Analyzing Binomial Probability in Automobile Accidents and Stolen Car Recoveries

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Presentation Transcript

  1. Notes Over 12.6 Finding a Binomial Probability 1. An automobile safety engineer claims that 10% of automobile accidents are due to driver fatigue. Suppose you randomly surveyed 6 people who had been in an accident. What is the probability that exactly 3 of them were due to driver fatigue?

  2. Notes Over 12.6 Finding a Binomial Probability 2. The probability that a stolen car will be recovered is 63%. Find the probability that exactly 4 of 5 stolen cars will be recovered?

  3. Notes Over 12.6 Constructing a Binomial Distribution 3. Draw a histogram of the binomial distribution in Exercise 1. Find the probability that at most 3 of the accidents were due to driver fatigue.

  4. Notes Over 12.6 Constructing a Binomial Distribution 3. Draw a histogram of the binomial distribution in Exercise 1. Find the probability that at most 3 of the accidents were due to driver fatigue. 0.5 0.4 0.3 0.2 0.1 0 0 1 2 3 4 5 6

  5. Notes Over 12.6 Constructing a Binomial Distribution 4. Draw a histogram of the binomial distribution in Exercise 2. Find the probability that at least 2 of the stolen cars will be recovered.

  6. Notes Over 12.6 Constructing a Binomial Distribution 4. Draw a histogram of the binomial distribution in Exercise 2. Find the probability that at least 2 of the stolen cars will be recovered. 0.4 0.3 0.2 0.1 0 0 1 2 3 4 5

  7. Notes Over 12.6

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