Suppose that the reject rate of a product is 0.005, take any 1000 pieces from this batch of products, and calculate the probability that the reject rate is not greater than 0.007 eight thousand one hundred and fifty-nine

Suppose that the reject rate of a product is 0.005, take any 1000 pieces from this batch of products, and calculate the probability that the reject rate is not greater than 0.007 eight thousand one hundred and fifty-nine

The number of scrap in 1000 products X ~ B (1000,0.005),
EX=5,DX=4.975.
Among them, the scrap rate is not more than 0.007, that is, the number of scrap is not more than 7.007
According to the central limit theorem,
Y = (X-5) / √ 4.975 approximately obeys the standard normal distribution,
P(X≤7)=P(Y≤(7-5)/√4.975=0.8967)
=Φ(0.8967)=0.8150.
Your answer is p (x ≤ 7) = P (Y ≤ 0.90) = Φ (0.90) = 0.8159