general

Consider the sampling distribution of a sample mean obtained by random sampling from an infinite population. This population has a distribution that is highly skewed towards the large values.
How is the mean of the sampling distribution related to the mean of the population?
How is the standard deviation of the sampling distribution related to the standard deviation of the population?
How is the shape effected by the sample size?

An opinion poll asks an SRS of 500 adults whether they favor giving parents of school-age children vouchers that can be exchange for education at any public or private school of their choice each school would be paid by the government on the basis of how many vouchers it collected. Suppose that in fact 45% of the population favor the idea, find the probability that more than half are in favor. 

Canada bauxite ore is moved into things;;; When functioning properly, the actual weights of ore loaded into each car by the filling equipment at the mine are approximately normally distributed with a mean of 70 tons and a standard deviation of 0.9 ton. If the mean is greater that 70 tons, the loading mechanism is overfilling. 
If the filling equipment is functioning properly, what is the probability that the weight of the ore in a randomly selected car will be 70.7 tons or more? Show your work.
Suppose that the weight of the ore in a randomly selected car is 70.7 tons. Would that fact make you suspect that the loading mechanism is overfilling the cars? Justify your answer. 
If the filling equipment is functioning properly, what is the probability that a random sample of 10 cars will have a mean ore weight of 70.7 tons or more? Show your work. 
Based on your answer in part (c), if a random sample of 10 cars had a mean ore weight of 70.7 tons, would you suspect the loading mechanism was overfilling the cars? Justify your answer. 

Suppouse that the distribution of adult weight is somewhat right-skewed with a mean of 175 pounds and a standard deviation of 25 pounds. A large elaveator has a weight limit of 7200 pounds if 40 adults enter what is the probability it exceeds the limit?