To solve this problem, we need to use the binomial distribution, which is a probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has the same probability of success.
Let's define the following variables:
X: the number of red candies in an 8 oz package
n: the total number of candies in the package (250)
p: the probability of getting a red candy (0.2)
The probability of getting less than 45 red candies can be calculated as follows:
P(X < 45) = Σ(k=0 to 44) (n choose k) * p^k * (1-p)^(n-k)
where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n items.
Using a calculator or statistical software, we can calculate this probability to be approximately 0.00026, or 0.026%. This means that there is a very low probability of getting less than 45 red candies in an 8 oz package.
the average proportion of red candies in a pakage is 20% and an 8 oz package contains about 250 candies.What is the probability that a randomly selected 8 oz bag contains less than 45 red candies?
2 answers
Therefore, if a package has less than 45 red candies, it may be considered to be defective or not meeting the expected standards. The manufacturer may need to investigate the cause of this issue and take corrective actions to improve the quality of their product.