Salaries for teachers in a particular state have a mean of S 4?000 and a standard deviation of S 415-013. Hint for parts a and b a. If we randomly select 14 teachers from that district, can you determine the sampling distribution of the sample mean? Nov if yes, what is the name of the distribution [one word]? [if no, leave these three blank] The mean?I I The standard error? I I b. If we randomly select SCI 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?I I The standard error? I I 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 51.?" d. Assuming a sample size of ED, what is the probability that the sampling error is within 51 DOD. [In other words, the sample mean is within Sl of the true mean.) Hint for d Hint for e and f e. Assuming a sample size of SCI, what is the 90th 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? 3' Next