In a sample of 8 high school students, they spent an average of 28.8 hours each week doing sports with a sample standard deviation of 3.2 hours. find the 95% confidence interval, assuming the times are normally distributed.

Step-by-step explanation:

Since the population standard deviation is unknown, and the sample standard deviation , must replace it, the distribution  must be used for the confidence interval.

The sample size is n=8.

The degree of freedom is , .

With 95% confidence level, the (significance level) is 5%.

Hence with 7 degrees of freedom, . (Read from the t-distribution table see attachment)

The 95% confidence interval can be found by using the formula:

.

The sample mean is hours.

The sample sample standard deviation is hours.

We now substitute all these values into the formula to obtain:

.

We are 95% confident that the population mean is between 26.12 and 31.48  hours.

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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