Salaries for teachers in a particular state have a mean of S 51000 and a standard deviation of S 6800. Hint for parts a and b What does the Central Limit Theorem tell you about how the i? is distributed and if we know nothing about the original distribution what does the sample size need to be in order for its E to be normal? a. If we randomly select 38 teachers from that district, can you determine the sampling distribution of the sample mean? If yes, what is the name of the distribution [one word)? {if no, Leave these three blank} The mean? The standard error? b. If we randomly select 20 teachers from that district, can you determine the sampling distribution of the sample mean? If yes, what is the name of the distribution [one word)? {if no, Leave these three blank] The mean? The standard error? c. For which sample size would I need to know that population distribution of X, teacher salaries, is normal in order to answer? Hint for part c Again think about the Central Limit Theorem, for which part above, a or b, did you say that no, you could not determine the sampling distribution of the sample mean? That is the one in which you'd have to assume normality of the original distribution or at least a symmetric distribution in order to establish normality of the sampling distribution of the sample mean. d, Assuming a sample size of 38, what is the probability that the sampling error is within $1000. [In other words, the sample mean is within $1000 of the true mean.) Hint for d So this is asking what is the probability that the E is between $1000 below the true mean to $1000 above the true mean, which is given in the beginning of this problem [just don't forget to use the standard error of :E to find this probability.) Hint for e and 1' 0th e, Assuming a sample size of 38, what is the 9 percentile for the AVERAGE teacher's salary? 'F. Assuming that teacher's salaries are normally distributed, what is the 90th percentile for an INDIVIDUAL teacher's salary