QUESTION 1
(a) Explain following terms-
(i) Distinct random variable
(ii) Continuous random variable
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3.98
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4.08
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5.47
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5.79
|
5.64
|
|
4.9
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6.17
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6.68
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8.02
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8.01
|
(i) Calculate the mean, median, mode, first quartile and third quartile.
(ii) Calculate the range and the interquartile range.
(iii) Calculate the variance, standard deviation and the coefficient of variation.
(iv) Using above data construct a Box and Whisker plot.
(v) A new household installs a water metre and would like to know its water consumption. A neighbour replies, ‘almost certainly not more than 5 metres cube’. On the basis of the results of (a) and (b), evaluate the accuracy of this statement.
QUESTION 2
Many internet users shopped online during the year 2010 summer holidays. A sample of 200 customers indicated the following information as to whether they were satisfied with the experience or received the products on time:
|
|
Received products on time
|
|
Satisfied with the experience
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Yes
|
No
|
|
Yes
|
60
|
60
|
|
No
|
15
|
65
|
(a) Give an example of a simple event.
(b) Give an example of a joint event.
(c) What is the complement of being satisfied with the experience?
(d) If a customer is selected at random, what is the probability that
(i) The customer is satisfied with the experience?
(ii) The customer receives the product on time?
(iii) The customer receives the product on time and is satisfied with the experience?
(iv) The customer does not receive the product on time and is not satisfied with the experience?
(v) The customer is satisfied with the experience or receives the product on time?
(vi) The customer is not satisfied with the experience or received the products on time?
QUESTION 3
(a) BCL Law School wants to identify how successful its graduates are at passing bar exam on the first try. Two hundred graduates are randomly selected and asked whether they passed the bar exam first time they took it. Of the 200 graduates, 130 said they passed the exam on the first try.
(i) Set a 98 percent confidence interval for proportion of law student graduates at this university who passed the bar exam. Construe the interval in the context of the problem.
(ii) Give a possible source of bias in this study.
(b) A questionnaire of expenses habits was given to a random sample of college students. Each student was asked to documentation and report the amount of money they spent on textbooks in a semester. The sample of 130 students resulted in an average of $422 with standard deviation of $57.
(i) Give a 90 percent confidence interval for the mean quantity of money spent by college students on textbooks.
(ii) Is it true that 90 percent of the students spent the amount of money found in the interval from part (i)? Clarify your answer.
(iii) What is the margin of error for the 90 percent confidence interval?
(iv) How many students have to you sampled if you want a margin of error of $5 for a 90 percent confidence interval?