Suppose the weights of male adults are known to have a normal distribution with mean 70 kg and standard deviation 12 kg

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Suppose the weights of male adults are known to have a normal distribution with mean 70 kg and standard deviation 12 kg.

a. What is the population of interest in this problem?

b. Suppose we are to take a random sample of 10 adults from this population. Explain why we can safely ignore the finite population correction factor in our calculation of the standard deviation of the sample mean, even if the population is finite.

C. Calculate the expected value and the standard error for the mean of the above sample of 10

d. An old elevator has a posted carrying capacity of 750 kg. If ten randomly selected adults from this population enter the elevator, what is the probability that their total weights exceed the elevator's capacity?

e. If the distribution of weights was not normal, would the expected value and the standard error in part (c) be still valid? How about the probability in part (d), would it still be approximately correct? Explain your answer.