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Questions and Answers
What is the probability of selecting exactly 2 defective televisions from a sample of 7?
What is the probability of selecting exactly 2 defective televisions from a sample of 7?
Using the Hypergeometric Distribution, how many non-defective televisions are selected in the probability calculation for exactly 2 defective televisions?
Using the Hypergeometric Distribution, how many non-defective televisions are selected in the probability calculation for exactly 2 defective televisions?
Which of the following correctly represents the formula for calculating the probability of selecting 2 defective televisions?
Which of the following correctly represents the formula for calculating the probability of selecting 2 defective televisions?
What is the result for the probability of selecting at least 2 defective televisions?
What is the result for the probability of selecting at least 2 defective televisions?
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What was likely incorrect or incomplete about calculating P(X ≥ 30)?
What was likely incorrect or incomplete about calculating P(X ≥ 30)?
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Study Notes
Probability of Defective Televisions
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A sample of 7 televisions (n=7) is randomly selected from a batch of 200 (N=200).
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15 of the 200 televisions are defective.
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The probability of selecting 2 defective televisions is calculated using the hypergeometric distribution.
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The formula for the probability is: P(X≥2) = Σ (x=2)^∞ [ (15 𝑥) (200 - 15) (7-x) / (200)⁷ ]
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Calculating P(X=2):
- P(X=2) = (15 2) (200-15) (7-2) / (200)⁷ = 0.0786
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Calculating P(X≥2) (for x = 2 to infinity using summation):
- P(X≥2) = 0.09
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Calculating another part of the problem:
- P(X ≥ 2) using summation for X values of 30 to infinity :
- P(X≥2) = 0.01
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Calculating probability of X less than or equal to 2 using summation notation:
- P(X ≤2) = 0.99
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Description
This quiz explores the calculation of the probability of selecting defective televisions from a batch. Using the hypergeometric distribution, you will compute probabilities for selecting 2 or more defective televisions in a random sample. Test your understanding of probability concepts in this scenario!
