Data on salaries in the public school system are published annually by a teachers' association. The mean annual salary of (public) classroom teachers iz 53 4 thousand. Assume a standard deviation of $58.2 thousand. Complete parts (a) through (&) below. 8. Determine the sampling distribution of the sample mean for samples of size 64. The mean of the sample mean is Hs = $|:|. {Type an integer or a decimal. Do not round.) The standard deviation of the sample mean is o; = $|:|. {Type an integer or a decimal. Do not round.) b. Detarmine the sampling distribution of the sample mean for samples of size 256. The mean of the sample mean is p; = $|:|. {Type an integer or a decimal. Do not round.) The standard deviation of the sample mean is o= $|:|. {Type an integer or a decimal. Do not round.) c. Do you need to assume that classroom teacher salaries are normally distributed to assume the distributions in parts (a) and (b) are normally distributed? Explain your answer. (O A. No, because if x is normally distributed, then x must be normally distributed. (O B. Yes, because the sample sizes are not sufficiently large so that x will be approximately normally distributed, regardless of the distribution of x. (O C. Yes, because x is only normally distributed if x is normally distributed. @ D. No, because the sample sizes are sufficiently large so that x will be approximately normally distributed, regardless of the distribution of x. d. What is the probabhility that the sampling error made in estimating the population mean salary of all classroom teachers by the mean salary of a sample of 64 classroom teachers will be at most 310007 (Round to three decimal places as needed.) e. What is the probability that the sampling arror made in estimating the population mean =alary of all classroom teachers by the mean salary of a sample of 256 classroom teachers will be at most 310007 (Round to three decimal places as needed.)