A machine making electrical resistors has a probability of.1 that the values wil

Question

A machine making electrical resistors has a probability of.1 that the values will fall outside of the target range. 20 resistors are chosen at random. a. What is the probability that 5 of the resistors fall outside of the target range? b. What is the probability that less than 2 resistors fall outside of the target range? How many resistors should be expected to fall outside of the target range? c. d. What is the standard deviation for the number of resistors that fall outside of the target range? If the machine produced 14 resistors that are outside of the target range, would this be convincing evidence that the original claim of.1 is incorrect? Explain. e.

Explanation / Answer

n = 20

P = 0.1

It is a binomial distribution

P(X = x) = nCx * p^x * (1 - P)^(n - x)

a) P(X = 5) = 20C5 * (0.1)^5 * (0.9)^15 = 0.0319

B) P(X < 2) = P(X = 0) + P(X = 1)

= 20C0 * (0.1)^0 * (0.9)^20 + 20C1 * (0.1)^1 *(0.9)^19 = 0.3917

C) Expected number of resisters = n * P = 20 * 0.1 = 2

D) Standard deviation = Sqrt(np(1 - p)) = Sqrt(20 * 0.1 * 0.9) = 1.3416

E) P(X = 14) = 20C14 * (0.1)^14 * (0.9)^6 = 0.00001

Since the probability value is less than 0.05, so it would be convincing evidence that the original claim of 0.1 is incorrect.

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