In a tire factor the quality control inspector examines a ra

In a tire factor, the quality control inspector examines a randomly chosen sample of 9 tires. When more than one defective tire is found, production is halted, the existing tires are recycled, and production is then resumed. The purpose of this process is to ensure the defect rate is no more than 11%. Occasionally, by bad luck, even if the defect rate is no more than 11%, more than one defective tire is found from the chosen 9.
What percent of the time does this happen?

Assume the defect rate is equal to 11%.

Solution

x - \"number of defect tires out of 15\"
prob of pass is (.94)

Find P(x>2)

so 1 - P(x<=1) = 1 - { p(x=0) + p(x=1) }
= 1 - { (.94)^16 + 16c1*(.06)^1*(.94)^15 }
= 1 - .77376
= .23