The director of quality of a company manufacturing heavy fabrics is interested in studying the warpwise breaking strength of fabric. breaking strength is known to be approximately normally distributed. the following data represent the warpwise fabric breaking strengths (in pounds per square inch) for a random sample of 25 pieces:
196.5 198.1 192.1 200.1 203.2 202.9 207.3 201.7 207.5 207.7 195.5 198.4 192.3 189.9 196.1 197.9 202.4 189.9 198.1 204.7 205.3 189.5 202.1 210.2 196.9
(a) calculate a 99% confidence interval that estimates the average breaking strength for all such fabric pieces.
(b) calculate a 99% tolerance interval for the breaking strength that will include 95% of all the fabric pieces.

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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c) the x-coordinate of the center of the circle increases by 3