Question

Suppose 30 out of 500 components for a computer were found defective. At this rate how many defective components would he found in 1600 components? ​

Answer 1

Step-by-step explanation:

Distribution of samples to be defective is [math]Bin(200, 0.05)[/math].

We need to calculate [math]P(X>4) = 1 - P(X<=4)[/math].

[math]P(X<=4) = P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)[/math]

For binomial distributed random variable [math]Bin(n, p)[/math],

[math]P(X=k) = \dbinom{n}{k}p^{k}(1-p)^{n-k}[/math]

Now you can plug the values and calculate the probability.

Approch II:

We can use Poisson approximation to the Binomial distribution.

Here, [math]\lambda = np = 200*0.05 = 10[/math].

For [math]Pois(\lambda)[/math],

[math]P(X=k)=e^{-\lambda}\frac{\lambda^{k}}{k!}[/math]

So,

[math]\begin{align}P(X<=4) &= P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4) \\ &= e^{-10}\frac{10^{0}}{0!} + e^{-10}\frac{10^{1}}{1!} + e^{-10}\frac{10^{2}}{2!}+e^{-10}\frac{10^{3}}{3!}+e^{-10}\frac{10^{4}}{4!}\end{align}[/math]

Now you can calculate [math]P(X>4)[/math]

hope it helps you

Answer 2

Answer: In this case : n = 200 (total items) p = Probability of defective = 5/100 = 0.05 X ... If a sample of 200 items is taken at random from the production find the ... the supervisor of the shop floor picked up an item and found that it was defective. ... What is the probability that exactly one box contains exactly one defective component?

Step-by-step explanation:

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