1. a. How to construct confidence interval for population mean. b. .A manufacturer of television picture tubes tested 80 tubes to determine their mean lifetime. The sample yields an average of 4500 hours with a standard deviation of 450 hours. Determine a 98% confidence interval for the population mean. 2. Give a real life example of simple random sampling and convenience sampling. 3. A traffic control officer reports that 70% of the trucks passing through a check post are from out of thr Dhaka city. What is the probability that at least four of the next six trucks are from the out of the city? 4. The incidence of occupational disease in an industry is such that the workers have 23% chance of suffering from it. What is the probability that out of 9 workers 7 or more will contract the disease? 5. As a result of tests on 18000 electric fans manufactured by a company, it was found that lifetime of the fans was normally distributed with an average life of 2050 hours and standard deviation of 60 hours. On the basis of the information, estimate the number of fans that is expected to run for more than 2160 hours. 6. The Philips Bangladesh manufactures electric bulbs that have a length of life that is normally distributed with mean equal to 830 hours and standard deviation of 30 hours. Find the probability that a bulb burns between 740 and 840 hours. 7. a. From the following statements, write the null hypothesis and alternative hypothesis. Also identify which is the claim. i. The average height of SEU students is greater than 5'7". ii. A research organization reports that 9% of all adult grocery shoppers in the U.S never buy the store board. iii. A local chess club claims that the length of time to play a game has a standard deviation of more than 23 minutes. iv. Fewer than 5% of adults ride the bus to work in Los Angeles. b. A bulb manufacturing company claims that the average longevity of their bulb is 3.52 years with a standard deviation of 0.13 years. A random sample of 45 bulbs gave a mean longevity of 3.67 years. Does the sample mean justify the claim of the manufacturer? Use a 1% level of significance