Data on salaries in the public school system are published annually by a teacher

Question

Data on salaries in the public school system are published annually by a teachers' association. The mean annual salary of (public) classroom teachers is of $8.0 t b. Determine the sampling distribution of the sample mean for samples of size 256 The mean of the sample mean is $ 55,400. (Type an integer or a decimal. Do not round.) The standard deviation of the sample mean is a $ 500 (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 0 A. Yes, because x is only normally distributed if x is normaly distributed No, because the sample sizes are su ciently large so that x will be approximately normally distributed regardless or the distribution of X O c Yes, because the sample sizes are not sufficient y large so that x will be approximately normally distributed regardless of the distribution of x 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 Round to three decimal places as needed.)

Explanation / Answer

d)

for normal distribution z score =(X-)/ here mean=       = 55400 std deviation   == 8000.000 sample size       =n= 64 std error=x=/n= 1000.0000

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