Sam works at the JJ Electronics Factory. JJ produces the A23 electronic component. The length, X, of an A23, is normally distributed with a meanμ = 10 centimeters and a standard deviation o = 0.53 centimeters. Sam randomly selects 20 A23 components from the production line for quality control purposes and measures their lengths. Let M be the sample mean length of the measured A23 components. Let S be the total length of the measured A23 components. (i.e. sum of the 20 lengths. a) What is the probability that X < 10.5? .6915 b) What is the probability that X > 10.5? .3085 c) What is the probability that all of the 20 measurements are less than 11? .0171 d) What is the expected value of S? 200 e) What is the standard deviation of S? 2.37 f) What is the probability that S-200 >2? 1.99 g) What is the standard deviation of S-200 2.37 h) What is the expected value of M? 10 i) What is the standard deviation of M? .1187 j) What is the probability that M >10.1? .199 k) What is the standard deviation of 9M? 1.068 I) If the probability of X >k is equal to .8, then what is k? 10.446

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Please complete all work in excel.  Use excel to make any necessary calculations and be sure to identify the answer, including units (if necessary). Answers that need formulas must have them within the answer cell. A manager is trying to educate employees on the effects of personal health and workplace performance. The manager has gathered data from a group of employees to evaluate the effects of sleep and sickness.  The manager asked employees to record the total number of hours of sleep they had over 10 working days in two weeks and compared it to the number of sick days that each took over those 10 days. Sick Days Total hours of sleep 0 80 2 40 1 60 0 70 3 50 2 90 4 35 1 68 0 72 2 55   The manager wonders if a non-linear model is a better relationship between the variables. Develop the model and run a regression adding the non-linear variable for total hours of sleep.

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