Scores of 50 college students who have taken a statistics test has a mean of 82 and a standard deviation of 5. Construct a 99 % confidence interval for the mean score. Also, report the critical value LaTeX: z_cz c corresponding to a confidence level of c

(80.1786, 83.8214)

Step-by-step explanation:

Confidence interval for population mean is given by :-

, where = Sample mean , n= sample size , = standard deviation, = critical z-value.

Given: n= 50,   ,

Critical z-value for 99% confidence level = 2.576

Now, a 99 % confidence interval for the mean:

Hence, required 99% confidence interval = (80.1786, 83.8214)

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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