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2 answers:
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Answer:
a) The approximate probability that more than 25 chips are defective is 0.1075.
b) The approximate probability of having between 20 and 30 defecitve chips is 0.44.
Step-by-step explanation:
Lets call X the total amount of defective chips. X has Binomial distribution with parameters n=1000, p =0.02. Using the Central Limit Theorem, we can compute approximate probabilities for X using a normal variable with equal mean and standard deviation.
The mean of X is np = 1000*0.2 = 20, and the standard deviation is √np(1-p) = √(20*0.98) = 4.427
We will work with a random variable Y with parameters μ=20, σ=4.427. We will take the standarization of Y, W, given by
The values of the cummmulative distribution function of the standard normal random variable W, which we will denote , can be found in the attached file. Now we can compute both probabilities. In order to avoid trouble with integer values, we will correct Y from continuity.
a)
Hence the approximate probability that more than 25 chips are defective is 0.1075.
b)
As a result, the approximate probability of having between 20 and 30 defecitve chips is 0.44.