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General Instructions. Solve the following as required Show complete solution whenever possible. 1. A. local government ofcial observes an increase in the number of individuals with cardiovascular and obesityr pr1.645ohlems in his harangay. In order to improve the health conditions of his constituents, he aims to promote an easyr and cheap way to reduce weight. It is known that obesity results in risk of having ilhiesses like diabetes and heart problems. He encouraged his constituents to participate in his Dcnccfor Lye project every weekend for three months. To know if the program is effective in reducing weight, he randomly selected 12 participants from the group who completed the program. The weight loss data, in kilograms, of the 12 randomly selected participants after completing the program, are [1.5, I11", 11.9, 1.1, 1.2, 13, 1.4, 2.11, 2.3, 2.4, 2.1, and 3.11. It is known that the weight loss of those who have completed the dance program follows a normal distribution with variance of 3.24 Egg. a. (3me and interpret a 90% condence interval for the true mean weight loss of the participants who have completed the dance program. b. Calculate the width of the condence interval in {a.} c.. How many participants must he sampled in order to he 95% condent that the estimated mean weight loss of the participants will be within 8.5 kg of the true mean? 2. A manufacturer claims that the average content of a particular lubricant is ll] liters. The contents of a random sample of Ill containers were recorded as follows: [11.2, 93, 111.1, 111.3, 18.1, 9.8, 9.9, 111.4, 111.3 and 9.8 liters. Assume the distribution of contents is normal. Construct a 99% condence interval for .u. 3. The average entrance exam score of a random sample of 35 rst year students of [ISM was 89.66 with a standard deviation of 18.28. Find a 96% condence interval for the true mean score