Final answer:
To find the probability that at least 12 of the 14 randomly selected people have brown eyes, use the binomial probability formula. The probability can be calculated by subtracting the sum of the probabilities of having less than 12 people with brown eyes from 1. Whether it is unusual or not depends on the prevalence of brown eyes in the population.
Step-by-step explanation:
To find the probability that at least 12 of the 14 randomly selected people have brown eyes, we can use the binomial probability formula:
P(x ≥ k) = 1 - P(x < k),
where k is the value at which we want to calculate the probability.
In this case, we want to find the probability that at least 12 people have brown eyes, so k = 11.
Using the formula, we can calculate P(x < k) as follows:
P(x < 12) = P(x = 0) + P(x = 1) + P(x = 2) + ... + P(x = 11),
where P(x = k) is the probability of exactly k people having brown eyes. Given that the probability of an individual having brown eyes is 0.4, we can substitute this value into the formula and calculate the probabilities for each of the x values.
Finally, we can subtract this value from 1 to find P(x ≥ 12), which represents the probability that at least 12 people have brown eyes. Whether it is unusual to find at least 12 people with brown eyes out of a sample of 14 depends on the context and the background information we have. If the overall prevalence of brown eyes in the population is significantly lower than 40%, then it would be considered unusual. However, if the prevalence is similar to or higher than 40%, then it would not be considered unusual.