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Needed a Test for A packet of 10 electronic components is known to include 3 defectives. If 4 components are selected from packet at random, what is the expected value of the number of detective?A. 1.2B. 1.21C. 1.69D. 1.72?
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Needed a Test for A packet of 10 electronic components is known to inc...
The expected value of a random variable is given by the formula:
E(X) = Σ(x * P(x))
where X is the random variable, x is the possible values of X, and P(x) is the probability of X taking the value x.
In this case, let X be the number of defective components in the sample of 4. The possible values of X are 0, 1, 2, 3, and 4. We can find the probability of each value using the binomial distribution:
P(X = 0) = (7/10)^4 ≈ 0.24
P(X = 1) = 4 * (3/10) * (7/10)^3 ≈ 0.41
P(X = 2) = 6 * (3/10)^2 * (7/10)^2 ≈ 0.28
P(X = 3) = 4 * (3/10)^3 * (7/10) ≈ 0.07
P(X = 4) = (3/10)^4 ≈ 0.01
Using these probabilities, we can calculate the expected value of X:
E(X) = 0 * 0.24 + 1 * 0.41 + 2 * 0.28 + 3 * 0.07 + 4 * 0.01 ≈ 1.21
Therefore, the answer is B. 1.21.
E(X) = Σ(x * P(x))
where X is the random variable, x is the possible values of X, and P(x) is the probability of X taking the value x.
In this case, let X be the number of defective components in the sample of 4. The possible values of X are 0, 1, 2, 3, and 4. We can find the probability of each value using the binomial distribution:
P(X = 0) = (7/10)^4 ≈ 0.24
P(X = 1) = 4 * (3/10) * (7/10)^3 ≈ 0.41
P(X = 2) = 6 * (3/10)^2 * (7/10)^2 ≈ 0.28
P(X = 3) = 4 * (3/10)^3 * (7/10) ≈ 0.07
P(X = 4) = (3/10)^4 ≈ 0.01
Using these probabilities, we can calculate the expected value of X:
E(X) = 0 * 0.24 + 1 * 0.41 + 2 * 0.28 + 3 * 0.07 + 4 * 0.01 ≈ 1.21
Therefore, the answer is B. 1.21.
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Needed a Test for A packet of 10 electronic components is known to include 3 defectives. If 4 components are selected from packet at random, what is the expected value of the number of detective?A. 1.2B. 1.21C. 1.69D. 1.72? Related: Business Mathematics and Logical Reasoning & Statistics?
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