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A TV manufacturer knows that on an average 9% of their TV sets are defective. They sell these sets in shipments of 20 and guarantees that not more than one set will be defective. What is the probability that the shipment will meet the guaranteed quality? Enter your answer with at least two digits after the decimal, may use standard rounding rule.

Respuesta :

itzamirv2

Given:

- Probability of a TV set being defective = 9% = 0.09

- Number of TV sets in a shipment = 20

We want to find the probability of having 0 or 1 defective TV set in a shipment of 20. This can be calculated using the binomial probability formula:

For k = 0:

P(X=0) = (0.91)^20 ≈ 0.3542

For k = 1:

P(X=1) = 20 * 0.09 * (0.91)^19 ≈ 0.3767

Now, sum up these probabilities to find the total probability:

P(X ≤ 1) = P(X=0) + P(X=1)

Calculate each term:

P(X=0) ≈ 0.3542

P(X=1) ≈ 0.3767

Now, sum up:

P(X ≤ 1) ≈ 0.3542 + 0.3767

P(X ≤ 1) ≈ 0.7309

So, the probability that the shipment will meet the guaranteed quality is approximately 0.7309.

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