The assembly line that produces satellite radios has histori

The assembly line that produces satellite radios has historically resulted in a 3% defective rate.   A random sample of 1000 radios is drawn. What is the probability that the defective rate is greater than 5%? Suppose that in the random sample the defective rate is 5%.   What does that suggest about the defective rate on the assembly line?

Solution

Prob for any random to be defective p = 3% = 0.03

n = Sample size = 1000

X - no of defectives has each is independent and there are two outcomes.

As n is large and p is small we can use Poisson distribution with mean =np = 30

P(X>0.50) = 0.000298

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Instead of 3% if def rate is 5% np = mean = 50

P(X>50) = 0.4625