1. In each of the situations below an "experiment" is conducted. Determine whether or not the "experiment" is a binomial experiment. If so, explain (i) what a trial is, (ii) what a success is, (iii) what n and p are, and (iv) where the independence assumption comes in. If the experiment is not binomial, explain why not.
a. A company produces steel shafts for use in industry. It is known that 0.1% of the shafts are classified as scrap. A quality control inspector examines and classifies a random sample of 20 steel shafts.
b. A psychology test consists of 10 questions. The first five are true-false questions, the last five are multiple choice with four possible answers each. A student guesses the answer (that is picks an answer at random) for each of the 10 questions on the test.
c. A rare disease is genetic in origin. If a couple are both carriers of the disease there is a 25% chance that a child of theirs will be born with it. Whether or not one child has the disease has no bearing on the status of any other child. The couple plans to have three children.
d. Past experience has shown that 2% of the tax returns prepared by a firm contain errors. The manager of the firm plans to check a random sample of 30 returns.