A factory produces screws in batches of 100,000. The probability that a screw is defective is 0.01%. Assume that defects occur independently of each other.
(a) Approximate the probability that 15 or more screws in a batch are defective using the normal approximation to the binomial distribution.
(b) Approximate the probability that 3 or fewer screws in a batch are defective using the normal approximation to the binomial distribution.
(c) Approximate the probability that 3 or fewer screws in a batch are defective using the Poisson approximation to the binomial distribution.

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AlonsoDehner AlonsoDehner · Answer 1 · 2020-02-01T10:08:40+01:00

Answer:

Step-by-step explanation:

Given that a actory produces screws in batches of 100,000. The probability that a screw is defective is 0.01%

Let X be the no of screws defective

Assume that defects occur independently of each other.

a) When binomial approximated to normal mean = np = 1000 and

std dev = [tex]\sqrt{npq} \\=31.464[/tex]

[tex]P(X\geq 15) = P(X>14.5)\\= 0.99999999999999[/tex]

b) [tex]P(X\geq 3) =1[/tex] apprxoimately

c) When approximated to Poisson mean of poisson is 1000

P(X≥3) = 0.997231