Problem 7-32 An engineer has designed a modified welding robot. The robot will be considered good enough to manufacture if it misses only 1% of its assigned welds. And it will be judged a poor performer if it misses 5% of its welds. (In-between possibilities are not considered.) A test is performed involving 100 welds. The new design will be accepted if the number of missed welds R is 2 or fewer and rejected otherwise.(a) What is the probability that a good design will be rejected?
Probability=
(b) What is the probability that a poor design will be accepted?
Probability=

a. p= 0.0794 or 7.94%

b. p= 0.1183 or 11.83%

Step-by-step explanation:

a. This is binomial probability function expressed as:

where:

The probability of good design being rejected is equal to 1 minus a good design being accepted.

#Given p=0.01, n=100  this probability is calculated as:

Hence, the probability that a good structure is 0.0794 or 7.94%

b. The probability that a bad design is accepted is equivalent to the probability that at least two bad designs are accepted.

Given that p=0.05, n=100 and the x=0,1,2... the probability is:

Hence, the probability of a bad design being accepted is 0.1183 or 11.83%

step-by-step explanation: