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Part II
Q. 2
(a)Explain the classical definition of probability. [4]
(b)Three companies are bidding on a contract. The relative qualities of the companies are such that Company A is twice as good as Company B, and Company B is three times as good as Company C. what is the probability of each company winning the contract? [6]
(c)Given P(A)= 0.5 and P(A∪ B) = 0.7: [6]
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Q. 3
(a)Two machines A and B produce 45% and 55%, respectively of the total number of ball bearings produced by a certain factory. The percentages of defective output of these machines are 3% and 6%, respectively. If a ball bearing is randomly selected, find the probability that the item is defective. Find the probability that it was produced by the machine A. [10]
(b)Suppose that the probability of success in an oral interview for civil services is 0.32. If 10 candidates are being interviewed, [6]
(16)
Q. 4
(a)Assume that the weights (in pounds) of papers discarded each week by different offices in a large secretariat, are normally distributed with mean 9.43 and standard deviation 4.17 pounds. Find the probability that 5 randomly selected offices have mean discarded papers between 10 and 15 pounds. If an office is selected at random, what is the probability that it discarded less than 2 pounds paper during the last week? [8]
(b)The number of traffic accidents that occur on a particular stretch of road during a month follows a Poisson distribution with a mean of 6. What is the probability that on a randomly selected month, there are just 2 accidents on that road? Find the probability that the next two months will both result in four accidents each occurring on this stretch of road. [8]
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Q. 5
(a)Differentiate between Type-I and Type-II errors. [4]
(b)A sociologist develops a test to measure attitudes about public transportation, and 27 randomly selected subjects are given the test, Their mean score is 76.2 and their standard deviation is 21.4. Construct the 95% confidence interval for the mean score of all such subjects. [6]
(c)A researcher claims that not more than 65% officers in the public offices come on time in their offices. A random sample of 60 officers was taken on a random working day, It was observed that 37 officers were in time. Test the claim of the researcher at 5% level of significance. [6]
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Q. 6
(a)In an insurance study of worker's deaths in a heavy mechanical complex of a country, monthly fatalities are analysed for two different time periods. Sample data from the both time periods are summarized by the following statistics: n₁ = 12, x̄₁ = 46.42, s₁ = 11.07; n₂ =15, x̄₂ = 51.06, s₂ =10.39; At 0.05 level of significance, test the claim that both time periods have the same mean. [6]
(b)An exercise physiologist wants to decide whether a certain type of running program will reduce heart rates. He measures the heart rates of 10 randomly selected people who are then placed on the running program. One month later the exercise physiologist again measures the heart rates of the 10 people. The heart rates, both before and after the running program, are displayed as below: Before Program: 68, 76, 74, 71, 71, 72, 75, 83, 75, 74; After Program: 67, 77, 71, 70, 69, 70, 71, 77, 71, 74. Do the data provide sufficient evidence to conclude that the running program will reduce heart rates? (Use 5% level of significance.) [10]
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Q. 7
(a)What is the difference between a correlation problem and a regression problem? Also give the situation where we have to use partial correlation rather than simple correlation. [6]
(b)The general manager of an engineering firm wants to know whether a draftsman's experience influences the quality of his work? He selects 10 draftsmen at random and records their years of work experiences and their work quality rating (excellent = 5, very good = 4, good = 3, average = 2 and poor =1).The data recorded are given as follows: Experience: 1 17 20 9 2 13 9 23 7 10 Rating: 1 4 4 5 2 4 3 5 2 5 Find correlation coefficient between experience and rating. Also interpret the result. [10]
Not yet checked
(16)
Q. 8
(a)What are the advantages of sampling? Differentiate between random and non-random sampling. [6]
(b)What do you understand by sampling distribution? For a population of with elements 2, 4, 6, 8, 10, draw all possible random sample of size 2 without replacement and compute sample means. [10]
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Q. 9
Write note on any FOUR of the following:
(a)Mathematical expectation of a random variable [4]
(b)Applications of the Chi-square distribution [4]
(c)Analysis of variance (ANOVA) [4]
(d)Stratified random sampling [4]
(e)Applications of Statistics in the public health issues [4]
(f)Applications of Statistics in economic development [4]
The 2013 CSS Statistics paper set by the FPSC. Question wording only; questions marked “Not yet checked” have not been compared with the official paper yet.
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