Question

In problems below, all probabilities must be calculated using a TI83 or TI84 calculator or MS Excel. Be sure to list the calculator function in its entirety or the Excel command as your work for each problem. List the formulas for the mean and standard deviation as your work for those calculations as appropriate.

Part 3: Fender Bender The article, "Should You Report That Fender-Bender?" (Consumer Reports, 2013:15), reported that 7 in 10 automobile accidents involve a single vehicle. A random sample of 25 accident reports is selected.
Answer the following questions. Include your calculator functions or Excel commands for each probability question and round your answers to 4 digits.
a. What is the probability that exactly 8 accidents involve a single vehicle?
b.What is the probability that at most 13 accidents involve a single vehicle
c.What is the probability that at least 5 accidents involve a single vehicle?
d.What is the probability that fewer than 15 accidents involve a single vehicle?
e.What is the probability that more than 18 accidents involve a single vehicle?
f. Find the mean and standard deviation of the accidents that involve a single vehicle. Show your formula setup and your work. Use proper symbols.

Answer 1

To calculate the probabilities, you can use the binomial probability formula. Let's calculate the probabilities for each of the given questions using this formula.

Step-by-step explanation:

To calculate the probabilities using a TI83 or TI84 calculator or MS Excel, we can use the binomial probability formula:

P(X=k) = C(n, k) * p^k * (1-p)^(n-k)

where:

• P(X=k) is the probability of getting exactly k accidents involving a single vehicle
• C(n, k) is the combination of n items taken k at a time
• p is the probability of getting a single accident involving a single vehicle
• n is the number of accident reports selected

Let's calculate the probabilities for each of the given questions using the formula above:

a. Probability of exactly 8 accidents involving a single vehicle:

For this question, we have n=25 accident reports, so the probability is:

P(X=8) = C(25, 8) * (7/10)^8 * (3/10)^(25-8)

Using a calculator or Excel, evaluate this expression to get the probability.