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19 July, 02:46

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.

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  1. 19 July, 04:36
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    (B) Yes, because the probability of having 3 or more defective graphics cards is less than 0.10.

    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.
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