Question: A company manufactures a certain type of computer chip. A chip consists of three separate components A, B and C. In a quality control test; a chip passes if all three components pass. The probability that components A, B and C pass are 0.97, 0.79 and 0.88 respectively. An engineer must test a batch of 16 of these components.

(i) What is the probability that a chip passes a test? State any assumption you make in your answer.

For quality control purposes, the company uses an indexing system which attaches an index to the number of passes in each batch test as follows.

Let X be the number of passes in this batch test.

Using Excel or otherwise do the following;

(ii) Construct the probability distribution of X and produce a graph of the distribution.

(iii) Find its mean and standard deviation of the distribution of X

(iv) Find the expected quality control index for this batch test.