3. In the following situations, identify the random variable of interest (e.g. ”Let X be the...

3. In the following situations, identify the random variable of interest (e.g. ”Let X be the number of ...”). Then state whether or not the r.v. is binomial, justifying your answer.

(a) A police officer randomly selects 30 cars to find out how many do not have

a current Warrant of Fitness (WOF). She knows from experience that the

probability a car does not have a current WOF is 1.6

(b) A data collector goes from house to house in a Wellington suburb to find the number of houses where the person answering the door (over the age of 18) agrees with a particular housing policy of the current government. The probability that a randomly selected adult in New Zealand agrees with the policy is known to be 0.4. The collector will stop collecting responses once they have 100 responses.

(c) Mike is repeatedly rolling two dice and will stop when he gets a double six. He counts the number of rolls until he gets a ’success’.

Solutions

Expert Solution

a) The random variable of interest is number of cars which do not have a current Warrant of Fitness (WOF).

Note: It is given that probability a car does not have a current WOF is 1.6. If 1.6 is written correctly then random variable is not binomial. As 1.6 probability is not possible.

If probability a car does not have a current WOF is 0.6, then

This random variable is Binomial as each car is independent of the other and there are finite cars (30) only.

b) The random variable of interest is number of houses where the person answering the door (over the age of 18) agrees with a particular housing policy of the current government.

This random variable is Binomial as each house in indepedent of other and probability that a randomly selected adult in New Zealand agrees with the policy is 0.4 which is constant. Also there are finite 100 responses to be taken.

c) The random variable of interest X is number of rolls until he gets a double six.

As X can take infinite values like 2,3,4,.....

So X is not binomial.

milcah answered 1 month ago

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