Indira Gandhi National Open University (IGNOU) 2005 B.Tech Water Resource Engineering Mathematics II - Question Paper

Test Papers / Previous ques. Papers of IGNOU ET101 (B) Mathematics-II December 2005
B.Tech. Civil (Construction Management) /
B.Tech. Civil (Water Resources Engineering)
Term-End exam

December, 2005

ET-101(B) : MATHEMATICS-II
(Probability & Statistics)

Time: three hours
Maximum Marks: 70

Note : All ques. are compulsory. Use of calculator is followed. Use statistical table wherever necessary.
1. ans any 6 of the subsequent : (6x5=30)

(a) The chance that doctor A will diagnose a disease X is 6%. The chance that a patient will die by his treatment after accurate diagnosis is 40% and the chance of death by wrong diagnosis is 70%. A patient of doctor A who had disease X died. Whatis the chance that his disease was diagnosed correctly?

(b) Box A contains two white and four black balls. a different box B contains five white and seven black balls. A ball is transferred from the box A to the box B. Then a ball is drawn from the box B. obtain the probability that it is a white ball.

(c) obtain the errors in every of the subsequent statements. provide reasons also.

(i) The probability that it will rain tomorrow is 0.40 and the probability that it will not rain tomorrow is 0.52.

(ii) On a single draw from a deck of playing cards,the probability of selectng a heart is 1/4. the probabitity of selecting a black card is 1/2, and the probability of selecting both a heart and a black card is 1/8.

(d) Hoping to increase the chances of reaching a performance goal, the director of a research project has assigned 3 separate research teams the identical task. The director estimates that the team reliabilities are 0.9, 0.8, and 0.7 for successfully completing thetask in the allotted time. The task will be completed if any 1 team completes it in the allotted time. Assuming that the teams work independently, what is the probability that the task will not be completed in time ?

(e) A system consists of 3 identical components. Inorder for the system to perform as intended, all of the components must perform. every component has the identical probability of performance. If the system is to have a 0.92 probability of performing, what is the minimum probability of performance needed by every of the individual components ?

(f) Let E and F be 2 independent events. The probability that both E and F happen is 1/12 and the probability that neither E nor F happen is 1/2. obtain out P(E) and P(F).

(g) A learner takes his exam in 4 subjects P,Q, R, and S. He estimates his chances of passing in P as 4/5, in Q as 3/4, in R as 5/6 and in S as 2/3. To qualify, he must pass in P and at lowest 2 other subjects. What is the probability that he qualifies ?

(h) Police plan to enforce speed limits by using radar traps at four various locations within the city limits.The radar traps at every of the locations L1, L2, L3,and L4 are operated 40%, 30%, 20% and 30% ofthe time. If a person who is over-speeding on hisway to work has probabilities of 0.2, 0.1, 0.5 and 0.2 respectively of passing through these locations, what is the probability that he will receive a speeding ticket ?

2. ans any 2 of the subsequent : (2x10=20)

(a) A certain screw making machine produces an avg. of two defective screws out of 100 and packs them in boxes of 500. obtain the probability that a box contains 15 defective screws.

(b) A random sample of five units is opted from a steady stream of products from a punch press and the fraction defective is 0.10.

(i) What is the probability of one defective unit in the sample ?
(ii) What is the probability of one or less defective unit ?
(iii) Whai is the probability of two or more defective units ?

(c) If the probability that a heat-treating batch will be defective is 0.01, what is the probability of 2 defective batches out of 250 ? What is the probability of two or less ? Use Poisson distributor.

3. ans any 2 the following: (2x10=20)

(a) A group of 200 students has the mean height of 154 cm. a different group of 300 students has the mean height of 152 cm. Can these be from the identical population with standard deviation (S.D) of five cm ?

(b) A random sample of 16 values from a normal population is obtained to have a mean of 41.5 and standard deviation of 2.795. On this basis, is there any cause to reject the hypothesis that the population mean µ = 43 ? Also obtain the confidencelimits for µ.

(c) A manufacturer of sports equipment has developed anew synthetic fishing line that he claims has a mean breaking strength of eight kilograms with a standard deviation of 0.5 kilogram Test the hypothesis that µ = eight kilograms against the option that µ ? eight kilograms if a random sample of 50 fishing lines is tested and obtained to have a mean breaking strength of 7.8 kilograms. Use a 0.01 level of significance.

Earning:   Approval pending.