According to Chemical Engineering Progress (Nov. 1990), approximately 30% of all pipe work failures in chemical plants are caused by operator error.
(a) What is the probability that out of the next 20 pipe work failures at least 10 are due to operator error?
(b) What is the probability that no more than 4 out of 20 such failures are due to operator error?
(c) Suppose, for a particular plant, that, out of the random sample of 20 such failures, exactly 5 are operational errors. Do you feel that the 30% figure stated above applies to this plant Comment?

Question

According to Chemical Engineering Progress (Nov. 1990), approximately 30% of all pipe work failures in chemical plants are caused by operator error.
(a) What is the probability that out of the next 20 pipe work failures at least 10 are due to operator error?
(b) What is the probability that no more than 4 out of 20 such failures are due to operator error?
(c) Suppose, for a particular plant, that, out of the random sample of 20 such failures, exactly 5 are operational errors. Do you feel that the 30% figure stated above applies to this plant Comment?