From his stock of engines, the inventor selects a simple random sample of 50 engines for testing. The engines run for an average of 305 minutes. The true standard deviation is known and is equal to 30 minutes, and the run times of the engines are normally distributed. In R-studio, test the hypothesis that the mean run time is more than 300 minutes. Use a 0.01 level of significance.

The mean run time of the engines is greater than 300 minutes

Step-by-step explanation:

Null hypothesis: The mean run time of the engines is 300 minutes.

Alternate hypothesis: The mean run time of the engines is greater than 300 minutes.

Test statistic (Z) = (sample mean - population mean) ÷ sd/√n

sample mean = 305 minutes

population mean = 300 minutes

sd = 30 minutes

n = 50

Z = (305 - 300) ÷ 30/√50 = 5 ÷ 4.243 = 1.178

The test is a one tailed test. Using a 0.01 significance level, the critical value which is obtained from the standard normal distribution table is 2.326.

Conclusion:

Since the test statistic 1.178 is less than the critical value 2.326, reject the null hypothesis.

There is sufficient evidence to support the claim that the mean run time is more than 300 minutes.

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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rauschg

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step-by-step explanation:

answer: (c) m∠qpo + (2x + 16)° = 180°

step-by-step explanation:

the opposite angles of a quadrilateral are supplementary.

so, ∠o + ∠q = 180°   and   ∠p + ∠r = 180°

since ∠r = 2x + 16°, we can use substitution as follows:

∠p + ∠r = 180°

∠p + (2x + 16)° = 180°