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1. A machine is producing medical instrument and it is assumed that the standard deviation of the length of all the instruments is 100m. A sample of 200 instruments is selected and their average length is found to be 100cm. Determine the 95% condence interval for the population mean. (20 points) 2. The National Football League polls fans to develop a rating for each football game. Each game is rated on a scale from 0 to 100. The fan ratings for a random sample of 12 games are as follows: 57, 61, 85, 73. 71, 7'3. 20. 58. 80, 79, 84, 73 Determine and compute the point estimate of mean fan rating for the population of NFL games. (10 points) 3. The statistician of a certain university wants to know the mean of entering mathematics majors. He computed the mean age of 18 years old and a standard deviation of 1.4 years old on a random sample of 25 entering Mathematics majors coming from a normally distributed population. With 99% confidence, determine the interval estimate of the population mean. (20 points)