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Luden [163]
3 years ago
10

LabTech is a company that manufactures microscopes and other laboratory instruments . On occasion, one of the microscopes is def

ective when it comes off of the production line. The probability that a microscope is defective is 0.17%. Find the probability that one of the first 50 microscopes is defective .
Mathematics
1 answer:
Scrat [10]3 years ago
5 0

Answer:

0.0782 (7.82%)

Step-by-step explanation:

The required probability will be found by using the Binomial Distribution which fits the case of n independent events each with a probability of success equal to p with k successes.

The PMF (Probability Mass Function) is

f(k,n,p)=\binom{n}{k}p^kq^{n-k}

Where q = 1-p

LabTech states that the probability that a microscope is defective is 0.17%, p=0.0017, q=0.9983. We need to know the probability that k=1 microscope is defective out of a set of n=50 of them. We now apply the formula

f(1,50,0.0017)=\binom{50}{1}0.0017^10.9983^{49}=0,0782

Which means that there is a 7.82% of probability to get 1 defective microscope out of the first 50

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