When circuit boards used in the manufacture of compact disc players are tested, the long-run percentage of defectives is 5%. Let X = the number of defective boards in a random sample of size n = 20, so X ~ Bin(20, 0.05). (Round your probabilities to three decimal places.) (a) Determine P(X ≤ 2). (b) Determine P(X ≥ 5). (c) Determine P(1 ≤ X ≤ 4).

A First Course in Probability (10th Edition)
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ISBN:9780134753119
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Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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When circuit boards used in the manufacture of compact disc players are tested, the long-run percentage of defectives is 5%. Let X = the number of defective boards in a random sample of size n = 20, so X ~ Bin(20, 0.05). (Round your probabilities to three decimal places.)

(a) Determine P(X ≤ 2).


(b) Determine P(X ≥ 5).


(c) Determine P(1 ≤ X ≤ 4).


(d) What is the probability that none of the 20 boards is defective?


(e) Calculate the expected value and standard deviation of X. (Round your standard deviation to two decimal places.)

expected value      boards
standard deviation      boards
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