5. 500 eggs are taken at random from a large consignment, and 50 are found to be bad. Estimate thepercentage of bad eggs in the consignment and assign limits within which the percentage probably lies.Ans. 10%, 10 ± 3.96. A machine puts out 16 imprefect articles in a sample of 500. After the machine is repaired, puts out3 imprefect articles in a batch of 100. Has the machine been improved?Ans. The machine has not been improved.7. In a city A, 20% of a random sample of 900 school boys had a certain slight physical defect. Inanother city B, 18.5% of a random sample of 1600 school boys had the same defect. Is the differencebetween the proportions significant?Ans. z = 0.37, Difference between proportions is significant.8. In two large populations there are 30% and 25% respectively of fair haired people. Is this differencelikely to be hidden in samples of 1200 and 900 respectively from the two populations?Ans. z = 2.5, not hidden at 5% level of significance.9. One thousand articles from a factory are examined and found to be three percent defective. Fifteenhundred similar articles from a second factory are found to be only 2 percent defective. Can it reasonably beconcluded that the product of the first factory is inferior to the second?Ans. It cannot be reasonable concluded that the product ofthe first factory is inferior to that of the second.10. A manufacturing company claims 90% assurance that the capacitors manufactured by them willshow a tolerance of better than 5%. The capacitors are packaged and sold in lots of 10. Show thatabout 26% of his customers ought to complain that capacitors do not reach the specified standard.

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500 eggs are taken at random from a large consignment, and 50 are found to be bad. Estimate the percentage of bad eggs in the consignment and assign limits within which the percentage probably lies.