Skittles candies come in the colors red, orange, yellow, green, and purple, with each color having equal

Question:

Skittles candies come in the colors red, orange, yellow, green, and purple, with each color having equal probability. You are quality control inspector, and your job is to count up the number of purple candies in a random sample of 25 candies from a large population of candies coming down the factory line.
a. What is a "success" in this situation? What is the probability of a success on a single trial?
b. What is a "failure" in this situation? What is the probability of a failure on a single trial? ,
c. Explain in words what X is in terms of the story. What values can take?
d. Why is this a Binomial situation? What are the parameters?
e. What is the probability that you will find exactly 5 purple candies in your sample?
f. What is the probability that you will find at least 2 purple candies in your sample?
g. What is the expected number of purple candies in the sample?
h. What is the standard deviation in the number of purple candies in the sample?
i. If purple candies cost the company 1.5 cents each, with an additional general production fee of 25 cents (not related to the number of purple candies), what is the expected cost of purple candies for this sample?
j. What is the standard deviation of the cost of purple candies in this sample? Distribution
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