3. In each of the situations below an \"experiment\" is conducted. Determine whe

Question

3. In each of the situations below an "experiment" is conducted. Determine whether or not the "experiment" is a binomial experiment. If so, explain (1) what a trial is, (2) what a success is, (3) what n and p are. 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 produced 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) A mathematics student decided to toss a fair coin until he got two heads in succession. This was achieved after 12 tosses.

Explanation / Answer

(a)

Here probability of success remain constant and there is only two outcomes for each trials. So binomial experiment can be used.

(i)

Trials are 20 steel shafts

(ii)

The probability of success is 0.1%

(iii)

n = 20 and p =0.1%

(b)

Here probability of correct answer does not remain same for each quetion. SO it is not a binomial experiement.

(c)

Here chances that a child has disease is independent from other child and probability of having disease remain constant from child to child so binomial experiment can be used.

(i)

Number of children

(ii)

The probability of success is 25%

(iii)

n = 3 and p =25%

(d)

Here event need to occur two heads in a row. So probability of success does not same for each trial. That is it is a binomial experiment.

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