Answer: To solve this problem, we can use the binomial distribution formula. Let X be the number of blue jelly beans in a bag of 200 jelly beans. Then X follows a binomial distribution with parameters n = 200 and p = 0.15, where p is the probability of drawing a blue jelly bean.
The probability of getting more than 20% blue jelly beans in a bag can be calculated as:
P(X > 0.2*200) = P(X > 40)
We can use the normal approximation to the binomial distribution, since n is large (200) and p is not too close to 0 or 1. Using the mean and variance of the binomial distribution, we can calculate the corresponding mean and standard deviation of the normal distribution as follows:
μ = np = 200 * 0.15 = 30
σ = sqrt(np(1-p)) = sqrt(200 * 0.15 * (1-0.15)) = 4.07
Then, we can standardize the random variable X as:
Z = (X - μ) / σ
So, we have:
P(X > 40) = P((X - μ) / σ > (40 - μ) / σ)
= P(Z > (40 - 30) / 4.07)
= P(Z > 2.46)
Using a standard normal distribution table or a calculator, we find that P(Z > 2.46) is approximately 0.007. Therefore, the probability that a bag will contain more than 20% blue jelly beans is about 0.007 or 0.7%.
Explanation: