During the assembly of a certain piece of exercise equipment, 3 welds are requir

Question

During the assembly of a certain piece of exercise equipment, 3 welds are
required during different phases of the assembly process. It is assumed that the
welds are performed independently of one another. Due to variation in the
technique and materials used, only 97% of all welds are performed satisfactorily,
with the remaining 3% being classified as defective.
The production manager would like 95% of all pieces of this type of equipment to have
no defective welds. As such, the percentage of satisfactory welds must be increased. To
what value must the percentage be increased in order that exactly 95% of all pieces of
equipment have no defective welds?

Explanation / Answer

let probability of satisfactory weld =6

probability that   95% of all pieces of this type of equipment to have no defective welds =p3 =0.95

hence p=(0.95)1/3 =0.9830

hence % of satisfactory welds must be increased to 98.30%

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