Can you help me with these probability problems? -Confidence intervals for the mean To estimate the average time it takes to assemble a certain computer component, the supervisor of an electronics company took the time that 40 technicians took to perform this task. Obtaining a mean of 12.73 minutes and a standard deviation of 2.06 min. A) What can we say with 99% confidence about the maximum error, if X = 12.73 , is used as a point estimate of the average time required to perform the task ? B) use the data to construct a 98% confidence interval. C) with what confidence can we be sure that the sample mean does not differ from the actual measurement by more than 30 seconds ? -Hypothesis tests for the mean A sample of M brand cigars is tested and it is found that 50 of them have a mean of 17.5mg of tar, with a standard deviation of 2mg, can it be affirmed that the amount of tar in these M brand cigars meets the 17mg maximum standard requested by consumers? -Sampling distribution of the mean A random sample of size 36 is taken from a normal population that has a mean of 84 and a standard deviation of 12 What is the probability that the mean of this sample is: A) greater than 87 B) less than 82