High School

According to insurance records, a car with a certain protection system will be recovered 86% of the time. Find the probability that at least 8 out of 12 cars will be recovered.

Answer :

Final answer:

The problem can be solved using the concept of binomial probability and the binomial cumulative probability formula. Upon substituting the given values into the formula, we can use a graphing calculator or other software to calculate the desired probability.

Explanation:

This problem is based on the concept of binomial probability. The given details state that a car with a certain protection system will be recovered 86% of the time, therefore the probability of successful recovery, p, is 0.86. We need to find the probability that at least 8 out of 12 cars will be recovered.

Here's how to solve the problem:

  1. Using the binomial cumulative probability formula: P(X >= k) = 1 - binomcdf(n, p, k-1), where binomcdf is a cumulative probability function.
  2. Substitute the values into the formula: 1 - binomcdf(12, 0.86, 7).
  3. On using a graphing calculator or other software to calculate, we will derive the probability that at least 8 out of 12 cars will be recovered.

Learn more about Binomial Probability here:

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