Mechanical components are produced continuously in large numbers on a production line. When the machines are correctly adjusted, extensive data show that the proportion of defective components is...

Mechanical components are produced continuously in large numbers on a production line. When the machines are correctly adjusted, extensive data show that the proportion of defective components is 0.027. If the proportion of defectives in a sample of size 50 is so large that the result is significant at the 5% level, the production line will be stopped for adjustment.

a) What probability distribution applies?

b) What is the smallest proportion of defective items in a sample of 50 that will stop the production line?