According to a study, it takes an average of 330 minutes for taxpayers to prepar

Question

According to a study, it takes an average of 330 minutes for taxpayers to prepare, copy, and electronically file an income tax return. The distribution of times follows the normal distribution and the standard deviation is 80 minutes. A random sample of 40 taxpayers is picked. Use Appendix A.1 for the z-values. a. What is the standard error of the mean in this example? (Round your answer to 3 decimal places.) Error of the mean b. What is the likelihood the sample mean is greater than 320 minutes? (Round your answer to 4 decimal places.) Sample mean c. What is the likelihood the sample mean is between 320 and 350 minutes? (Round your answer to 4 decimal places.) Sample mean d. What is the likelihood the sample mean is greater than 350 minutes? (Round your answer to 4 decimal places.) Sample mean

Explanation / Answer

What does it mean the shape of the population? The shape distribution of the time should be gaussian bell (normal distribution). std of the mean = standard deviation / vn = 80 / v(40) = = v(160) = 12.65 T_m ~ N(330, 160) => X = (T_m - 330) / v(160) ~ N(0,1) P(T_m > 320) = P(X > (320-330)/v(160)) = = P(X > -0.79057) = 1 - F(-0.79057) = F(0.79057) = = 0.78541 P(320 1.66020) = 1- F(1.66020) = = 0.05262

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