A manufacturing machine has a 45% defect rate. If 129 items are chosen at random, answer the following. a) Which is the correct wording for the random variable? Select an answer b) Pick the correct symbol: n v - 129 c) Pick the correct symbol: p - 0.45 d) What is the probability that exactly 55 of them are defective? Round final answer to 4 decimal places. e) What is the probability that less than 55 of them are defective? Round final answer to 4 decimal places. f) What is the probability that more than 55 of them are defective? Round final answer to 4 decimal places. g) What is the probability that exactly 56 of them are defective? Round final answer to 4 decimal places. h) What is the probability that at least 56 of them are defective? Round final answer to 4 decimal places. i) What is the probability that at most 56 of them are defective Round final answer to 4 decimal places.

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Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.