MODULE-2
1. An analysis of monthly wages paid to workers in two firms A and B belong to the same industry gave the following results. (a) Which firm pays out large amounts as a wage bill? (b) In which firm there is greater variability in individual wages?
2. A university warehouse has received a shipment of 25 printers, of which 10 are laser printers and 15 are inkjet models. If 6 of these 25 are selected at random to be checked by a particular technician, what is the probability that exactly 3 of those selected are laser printers (so that the other 3 are inkjets)?
3. Each sample of water has a 10% chance of containing a particular organic pollutant. Assume that the samples are independent with regard to the presence of the pollutant. Find the probability that in the next 18 samples, at least 4 samples contain the pollutant.
4. Goals scored by two teams A and B in a football season were as follows:Find out which team is more consistent.
5. Out of 800 families with 4 children each, how many families would be expected to have (i) 2 girls and 2 boys (ii) at least one boy (iii) no girl (iv) at most two girls? Assume equal probabilities for boys and girls.
6. A microchip company has two machines that produce the chips. Machine I produces 65% of the chips, but 5% of its chips are defective. Machine II produces 35% of the chips and 15% of its chips are defective. A chip is selected at random and found to be defective. What is the probability that it came from Machine I?
7. Suppose that A and B are mutually exclusive events for which P (A) = 0.3 and P (B) = 0.5. What is the probability that 1. Either A or B occurs. 2. A occurs but B does not occur. 3. Both A and B occur?
8. Suppose that the time it takes the electronic device in the car to respond to the signal from toll plaza is normally distributed with mean 160 microseconds and standard deviation 30 microseconds. What is the probability that the device in the car will respond to a given signal within 100 to 180 microseconds
9. Explain Poisson Distribution.
10. If we randomly pick two television sets in succession from a shipment of 240 television sets of which 15 are defective, what is the probability that they will be both defective?
11. Suppose box A contains 4 red and 5 blue chips and box B contains 6 red and 3 blue chips. A chip is chosen at random from the box A and placed in box B. Finally, a chip is chosen at random from box B. What is the probability a blue chip was transferred from box A to box B given that the chip chosen from box B is red?
12. The number of defects in a thin copper wire follows Poisson distribution with mean of 2.3 defects per millimeter. Determine the probability of exactly two defects per millimeter of wire.
13. On a five-question multiple-choice test there are five possible answers, of which one is correct. If a student guesses randomly and independently, what is the probability that she is correct only on two questions?
14. Discuss properties of binomial distribution.
15. A random variable X has a Poisson distribution with a mean of 3. Find P (1 ≤ X ≤ 3)?
16. The following are the number of mistakes made in 5 successive days for 4 technicians working for a photographic laboratory: Technician I 6 14 10 8 11 Technician II 14 9 12 10 14 Technician III 10 12 7 15 11 Technician IV 9 12 8 10 11 Test at the level of significance α =0.01 whether the differences among the 4 sample means can be attributed to chance.
17. Suppose X is the normal distribution N(70, 4). Find P(X≥ 73)
18. Customers are used to evaluate preliminary product designs. In the past, 95% of highly successful products received good reviews, 60% of moderately successful products received good reviews, and 10% of poor products received good reviews. In addition, 40% of products have been highly successful, 35% have been moderately successful, and 25% have been poor products. a) What is the probability that a product attains a good review? If a new design attains a good review, what is the probability that it will be a highly successful product?
19. Type-I and Type-II error.
20. Statistical Population.
21. Bivariate Frequency Distribution.
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