a. Determine the sampling distribution of the sample mean for samples of size 64. The mean of the sample mean is uç =s 56.3|. (Type an integer or a decimal. Do not round.) The standard deviation of the sample mean is o =$ .95. (Type an integer or a decimal. Do not round.) b. Determine the sampling distribution of the sample mean for samples of size 256. The mean of the sample mean is uç =s 56.3|. (Type an integer or a decimal. Do not round.) The standard deviation of the sample mean is o; =S .475|. (Type an integer or a decimal. Do not round.) c. Do you need to assume that classroom teacher salaries are normally distributed to answer parts (a) and (b)? Explain your answer. O A. Yes, because x is only normally distributed if x is normally distributed. O B. No, because the sample sizes are sufficiently large so that x will be approximately normally distributed, regardless of the distribution of x. O C. Yes, because the sample sizes are not sufficiently large so that x will be approximately normally distributed, regardless of the distribution of x. O D. No, because if x is normally distributed, then x must be normally distributed. d. What is the probability 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 $1000? e. What is the probability that the sampling error made in estimating the population mean salary of all classroom teachers by the mean salary of a sample of 256 classroom teachers will be at most $1000? (Round to three decimal places as needed.)

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