Question

A computer graphics card manufacturer is testing an improvement to its production process. If a sample of 100 graphics cards manufactured using the new process has a less than 10% chance of having 3 or more defective graphics cards, then the manufacturer will switch to the new process. Otherwise, the manufacturer will stay with its existing process. If the probability of a defective graphics card using the new process is 0.9%, will the manufacturer switch to the new production process?

(A) Yes, because the probability of having 3 or more defective graphics cards is greater than 0.10.
(B) Yes, because the probability of having 3 or more defective graphics cards is less than 0.10.
(C) No, because the probability of having 3 or more defective graphics cards is less than 0.10.
(D) No, because the probability of having 3 or more defective graphics cards is greater than 0.10.

Answer 1

(B) Yes, because the probability of having 3 or more defective graphics cards is less than 0.10.

Step-by-step explanation:

Each graphics card using the new process has a 0.9% chance of failure.

the change for failure is then: 0.009 for a single unit among 100

Thus, the change for 3 units to fail within 100 is less than this.

As it must happen 3 times so 0.9% x 0.9% x 0.9% = 0.00729%

The project will be approved is the change is lower than 10%

Therefore, the project is viable.