9. A major automobile company was having trouble with the quality of paint on their grey cars. The first step was to collect data on the magnitude of the problem. Of 4063 recently painted grey...

Extracted text: 9. A major automobile company was having trouble with the quality of paint on their grey cars. The first step was to collect data on the magnitude of the problem. Of 4063 recently painted grey automobiles, 533 had paint problems that could casily be detected by visual inspection. Obtain a 95.7% confidence interval for the population proportion of defective grey paint jobs. 10. A manufacturer of a cell battery wants to determine the average lifetime of their brand new cell battery. (a) If he wants the maximum error to be at most 0.234 hours at 99.2% confidence level, what is the ideal sample size that he can take, by assuming that the standard deviation is 2.57 hours? (b) If a random sample of 175 cell batteries is taken, find the maximum error that can occur with 97% confidence level. (By assuming that the standard deviation remains unchanged). 11. Suppose that a researcher wants to estimate the percentage of all students whose CGPA is above 3.25. (a) If it can be presumed that the sample proportion (from a preliminary sample) is 0.73 and the maximum error that can be taken is 0.026, at 96.5% confidence level could you estimate the approximate sample size? (b) What is the approximate sample size for (a), if preliminary sample is not being considered?