Question 1
A random variable X has the following distribution:
x / 0 / 5 / 10P(X = x) / 0.4 / * / 0.3
(a). / Is X discrete or continuous? / [1 mark]
(b) / Fill in the gap marked by *. / [1 mark]
(c) / State the concept on which your answer to part (b) is based. / [1 mark]
(d) / Calculate the mean and the variance of this distribution. / [5 marks]
(e) Calculate P(X7).[2marks]
Question 2
The local Automobile Association conducted a study of the incidences over a ten-year period of children under the age of 5 years who were involved in motor vehicle accidents that resulted in road fatalities. The results for children who were not wearing set belts at the time of the accident are shown in the following table:
Age / Male / Female / Total0 / 265 / 227 / 492
1 / 204 / 191 / 395
2 / 367 / 207 / 574
3 / 316 / 190 / 506
4 / 477 / 194 / 671
Total / 1629 / 1009 / 2638
(a)Are these random variables discreteorcontinuous?[1mark]
(b)What is the probability that a fatality involved a3-yearold?[2marks]
(c)What is the probability that the fatality involved a child who is 3-year old and isamale?[2marks]
(d)What is the probability that the fatality involved a child who is a 3-year old or isamale?[3marks]
(e)What is the probability that the fatality involved a child who is 3-year old given that the childismale? [2marks]
(f)Two fatalities are randomly selected, what is the probability that the first fatality involved a child who is less than 1 year old and the secondfatality involved a child who is less than 1yearold? [3marks]
Question 3
Consider the following question and the proposed solution:
The Quality Manager of a battery manufacturing plant reviewed the warranty records within his department and found that 4% of the low maintenance batteries produced at the plant over the past 5 years were returned within the warranty period for a confirmed defect. Twelve low maintenance batteries were purchased at the plant last Saturday. What is the probability that more than 2 of these batteries will be returned to the plant within the warranty period with a confirmeddefect?
Critique the proposed solution. In your response, comment in: (1) the definition of the random variable X, (2) the suitability of the use of the binomial distribution, and (3) the working out of the answer.
State your answer to the question. Ensure that you define the random variable andshow all therelevantworking. [7marks]