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.

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:

Using the binomial cumulative probability formula: P(X >= k) = 1 - binomcdf(n, p, k-1), where binomcdf is a cumulative probability function.
Substitute the values into the formula: 1 - binomcdf(12, 0.86, 7).
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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