A toy manufacturer wants to know how many new toys children buy each year. A sample of 1417 children was taken to study their purchasing habits. Construct the 99% confidence interval for the mean number of toys purchased each year if the sample mean was found to be 7.7. Assume that the population standard deviation is 1.8. Round your answers to one decimal place.

The 99% confidence interval for the mean number of toys purchased each year is between 7.6 toys and 7.8 toys.

Step-by-step explanation:

We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:

Now, we have to find z in the Ztable as such z has a pvalue of .

So it is z with a pvalue of , so

Now, find M as such

In which is the standard deviation of the population and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 7.7 - 0.1 = 7.6 toys

The upper end of the interval is the sample mean added to M. So it is 7.7 + 0.1 = 7.8 toys

The 99% confidence interval for the mean number of toys purchased each year is between 7.6 toys and 7.8 toys.

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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step-by-step explanation: