1. The resistances of ten randomly selected 100-ohm resistors have been recorded: 79.9, 85.9, 87.0, 96.7, 107.4, 100.8, 115.4, 117.9, 98.0, and 102.6. The individual resistances are known to follow a normal distribution with a mean of 100 ohms and a standard deviation of 10 ohms. (a) Calculate the sample mean resistance associated with the ten resistors. (b) For a sample size of ten, find the prob of obtaining a sample mean as large as or larger than the one calculated in part (a). ( c ) For a sample size of ten, find the probability of obtaining a sample mean with a resistance between 95 and 105 ohms.

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answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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