(3) During your summer internship at a candy company, you are responsible for quality control on the foil-wrapping machine used to cover a certain type of chocolate. The machine individually wraps each chocolate in a piece of foil, and seals 25 wrapped chocolates into a box for sale. According to the manufacturer of the machine, the machine should successfully wrap any given chocolate with probability 0.95, independent of past performance. Your job is to go through five randomly selected boxes of chocolates, and count the number of defective chocolates in each box. (a) If the manufacturer is correct, explain why the number of defective chocolates in each box can be modeled with a Binomial random variable. (b) If the manufacturer is correct, what is the expected number of defective chocolates in any given box. (c) If the manufacturer is correct, what is the probability of finding 3 defectiv
(3) During your summer internship at a candy company, you are responsible for quality control on the foil-wrapping machine used to cover a certain type of chocolate. The machine individually wraps each chocolate in a piece of foil, and seals 25 wrapped chocolates into a box for sale. According to the manufacturer of the machine, the machine should successfully wrap any given chocolate with probability 0.95, independent of past performance. Your job is to go through five randomly selected boxes of chocolates, and count the number of defective chocolates in each box.
(a) If the manufacturer is correct, explain why the number of defective chocolates in each box can be modeled with a Binomial random variable.
(b) If the manufacturer is correct, what is the expected number of defective chocolates in any given box.
(c) If the manufacturer is correct, what is the probability of finding 3 defective chocolates or fewer in any given box.
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