Calculate the mean and the variance of this distribution

Reference no: EM131677999

INTRODUCTORY STATISTICS -

Assessment: Problem-Based Learning Scenario Set #1

Question 1 - A random variable X has the following distribution:

x	0	5	10
P(X = x)	0.4	*	0.3

(a) Is X discrete or continuous?

(b) Fill in the gap marked by *.

(d) Calculate the mean and the variance of this distribution.

(e) Calculate P(X < 7).

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	Total
0	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 discrete or continuous?

(b) What is the probability that a fatality involved a 3-year old?

(d) What is the probability that the fatality involved a child who is a 3-year old or is a male?

(e) What is the probability that the fatality involved a child who is 3-year old given that the child is male?

(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 second fatality involved a child who is less than 1 year old?

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 confirmed defect?

Let X be the number of batteries that were defective

X ~ Bin(12, 4%)

P(X = 2) = ¹²C₂(4%)¹⁰(96%)² = 6.378^-13

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 and show all the relevant working.

Reference no: EM131677999

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len1677999

10/13/2017 1:29:18 AM

Detailed Question: Assessment 2: Problem based learning Scenario Set#1. Weighing 10% is the only assignment that needs to be done. Questions 1-3. If there are any questions please feel free to ask me. Assessment 2, questions 1-3 only! Please and thank you! This coursework assignment is to be posted in the Problem-Based Learning Scenario #1 discussion forum. Thirty (30) minutes after posting your response, you will be able to view the responses posted by your group mates.

10/13/2017 1:29:12 AM

You are required to read the posts made by your peers and constructively comment on at least one of the posts. After reading the posts, feel free to initiate a discussion that will assist you in clarifying any misconceptions you may have. This is NOT a group assignment. It is expect that you will do your own work. Presentation of another person's work will be severely penalized.

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