A manufacturing company produces lenses for digital cameras. The defect rate for each lense is 9%. Which of the following testing procedures will result in more production stops?
Procedure A: The company will test 10 lenses per hour, and stops production if 2 or more lenses are defective.
Procedure B: The company will test 20 lenses per hour, and stops production if 4 or more lenses are defective.
I have no idea where to start.
To determine which testing procedure will result in more production stops, we need to compare the probabilities of stopping production under Procedure A and Procedure B.
Procedure A:
In Procedure A, the company tests 10 lenses per hour and stops production if 2 or more lenses are defective. This means that out of the 10 lenses tested, if 2 or more lenses are defective, production will stop.
To calculate the probability of stopping production under Procedure A, we need to calculate the probability of having 2 or more defective lenses out of 10. This can be done using the binomial distribution.
The formula for the probability of having exactly k successes in n trials, where the probability of success in each trial is p, is given by:
P(X = k) = (n choose k) * (p^k) * ((1-p)^(n-k))
In this case, n = 10 (lenses tested per hour) and p = 0.09 (defect rate for each lens). We want to calculate the probability of having 2 or more defective lenses, so we need to calculate the sum of probabilities for k = 2, 3, 4, ..., 10.
Procedure B:
In Procedure B, the company tests 20 lenses per hour and stops production if 4 or more lenses are defective.
Using the same approach as above, we need to calculate the probability of having 4 or more defective lenses out of 20.
Now, to determine which procedure will result in more production stops, compare the probabilities of stopping production under Procedure A and Procedure B. The procedure with the higher probability of stopping production would result in more production stops.
To calculate these probabilities, we can use the binomial distribution formula or a calculator that can perform binomial calculations.