Question

2. An automatic welding machine is being considered for use in a production process. It will be considered for purchase if it is successful on 99% of its welds. Otherwise, it will not be considered efficient. A test is to be conducted with a prototype that is to perform 100 welds. The machine will be accepted for manufacture if it misses no more than 3 welds. (a) What is the probability that a good machine will be rejected? (b) What is the probability that a machine with 97.5% welding success will be accepted? (c) What is the probability that an inefficient machine with 95% welding success will be accepted?

Answer 1

Solution:

Let X be the number of miss by the machine in performing 100 welds. The probability of success, p = 0.01 and X follows binomial distribution.

a. We have to find the probability X > 3

P (X > 3) = 1 - P (X 3)

= 1 - [P (X = 0) + P (X = 1) + P (X = 2) + P (X = 3)]

= 1 -

= 1 - (0.3660 + 0.3697 + 0.1849 + 0.0610)

= 1 - 0.9816

= 0.0184

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b.

We have to find the probability X > 3

P (X > 3) = 1 - P (X 3)

= 1 - [P (X = 0) + P (X = 1) + P (X = 2) + P (X = 3)]

= 1 -

= 1 - (0.0795 + 0.2039 + 0.2588 + 0.2168)

= 1 - 0.7590

= 0.2410

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c.

We have to find the probability X 3

P (X 3) =  [P (X = 0) + P (X = 1) + P (X = 2) + P (X = 3)]

=

= 0.0059 + 0.0312 + 0.0812 + 0.1396

= 0.2578