Based on past studies, a car manufacturer has found that 83% of new car buyers will sell their new car within the next four years. If 100 new car buyers are randomly selected, what is the probability that at least 90 will sell their cars within the next four years?

To find the probability that at least 90 out of 100 new car buyers will sell their cars within the next four years, we can use the binomial probability formula. The formula is as follows:

P(X >= k) = 1 - P(X < k)

Where P(X >= k) represents the probability of getting at least k successes, P(X < k) represents the probability of getting less than k successes, and P(X = k) represents the probability of getting exactly k successes.

In this case, we can set k = 90 and calculate P(X >= 90). However, before we can proceed, we need to determine the values for n, p, and q.

n represents the number of trials, which is the number of new car buyers selected, i.e., 100.

p represents the probability of success, which is the probability that a new car buyer will sell their car within the next four years, i.e., 83% or 0.83.

q represents the probability of failure, which is the probability that a new car buyer will not sell their car within the next four years, i.e., 100% minus the probability of success, or 1 - 0.83 = 0.17.

Now we can calculate the probability using the formula:

P(X >= 90) = 1 - P(X < 90)

To find P(X < 90), we need to calculate the cumulative distribution function (CDF) of the binomial distribution with parameters n = 100, p = 0.83, and q = 0.17.

Using statistical software, a calculator, or a binomial distribution table, you can calculate the probability of getting less than 90 successes out of 100 trials.

Once you have the value for P(X < 90), you can substitute it back into the formula to find P(X >= 90):

P(X >= 90) = 1 - P(X < 90)

This will give you the probability that at least 90 out of 100 new car buyers will sell their cars within the next four years.