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IET-I0l(B) I
B.Tech. Civil (Construction Management) I
B.Tech. Civil (Water Resources Engineering) I
B.Tech. (Aerospace Engineering) I

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Term-End Examination

U06l2 December, 2016
ET-101 MATHEMATICS-II (PROBABILITY AND STATISTICS)
Time: 3 hours Maximum Marks: 70
Note: All questions are compulsory. Use of scientific calculator is allowed. Use statistical tables wherever necessary.

1. Answer any six of the following: 6 x 5=30
Three salesmen, B and have been given a target of selling 10000 units of a particular product, the probabilities of achieving their targets being respectively 0.25, 0.30 and 0.50. If these three salesmen try to sell the product, find the probability of success of only one salesman and failure of the other two. Two computers, A and are to be marketed. A salesman who is assigned the job of finding customers for them has 60% and 40% chances respectively ,of succeeding in case of computers A and B. The computers can be sold independently. Given that he was able to sell at least one computer, what is the probability that the computer A has been sold? A product is assembled from two components, A and B. The probability of component A being defective is 0.03 and the probability of component B being defective is 0.02. What is the probability that the assembled product will not be defective? A problem in business statistics is given to 5 students, D and E. Their chances of solving it are 1/5 and 1/6 respectively. What is the probability that the problem will be solved A letter is chosen at random from the word 'PROFESSOR'. What is the probability that it is a vowel?

(ii) What is the probability that it is In a bolt factory, machines B1, B2 and B3 manufacture 25, 35 and 40 percent of the total output respectively. Of their outputs, 4 and 2 percent, respectively are defective bolts. A bolt is chosen at random and found to be defective. What is the probability that the bolt came from machine B3 A manufacturer produces IC chips, of which are defective. Find the probability that in a box containing 100 chips, no defectives are found. A marksman can hit a target 2 out of 3 times. In 4 shots, what are his chances of hitting it 3 or 4 times

2. Answer any two of the following: 2x10=20 A manufacturing company finds that 10 percent of its tools turnout to be defective in the production process. Find the probability that in a sample of 20 tools chosen at random, exactly 4 will be defective. Suppose in a normally distributed population, the average income per household is Rs.10,000 per month, with the standard deviation of Rs.800. A survey based on a random sample of 100 households is undertaken. What is the probability that the sample mean will be between Rs.9,800 and
Rs.10,100? A random sample of 100 students belonging to a college was taken. It was found that the mean height of these students was 168.75 cm. What should be the confidence intervals for estimating the mean height of the entire population of students at and assuming the population standard deviation as 7.5 cm?

3. Answer any two of the following: 2x10=20
A company is considering two different television advertisements for promotion of a new product. The management believes that advertisement A is more effective than advertisement B. Two test market areas with virtually identical consumer characteristics are selected. Advertisement A is used in one area and advertisement B in the other area. In a random sample of 60 customers who saw advertisement 18 tried the product. In a random sample of 100 customers who saw advertisement 22 tried the product. Does this indicate that advertisement A is more effective than advertisement if a level of significance is used A survey of 200 firms found the following evidence regarding productivity and market share:

Market Share

Productivity up to 10% 11-25% Total

Low 36 14 16 66
Medium 26 22 16 64
High 16 24 30 70
Total 78 60 62 200

Do you find that the above data gives you significant evidence to conclude that market share and productivity are related? Test the hypothesis at 0·01 level of significance. Metal conduits of 2 inch outer diameter are required by a construction company. To test whether the conduits procured by the company have the specified outer diameter, the following data on the outer diameter of 20 randomly selected conduits pieces are given:

1.97 2.09 2.24 3.17 1.01 2.87 1.34 1.79 3.89 4.16 3.01 1.62 2.81 3.10 2.59 2.75 1.10 0.57 2.05 1.67

Using the data perform an appropriate test at level of significance.