A random variable is normally distributed. It has a mean of 245 and a standard d

Question

A random variable is normally distributed. It has a mean of 245 and a standard deviation of 21. a.) For a sample of size 10, state the mean of the sample mean. b.) For a sample of size 10, state the standard deviation of the sample mean (the "sta error of the mean"). c.) For a sample of size 35, state the mean of the sample mean. d.) For a sample of size 35, state the standard deviation of the sample mean (the "standard error of the mean") e.) TRUE or FALSE: As sample size increases, standard deviation of the sample mean (the "standard error of the mean") also increases. For parts (a) through (d), enter answer in decimal form rounded to nearest thousandth (3 places 13.000 For part (e): Enter TRUE or FALSE after decimal), Examples of correctly entered answers: 0.000 0.004 0080 1200 0.594

Explanation / Answer

a) Mean of sample mean = 245

b) Standard error of the mean = sd / sqrt(n) = 21 / sqrt(10) = 6.641

c) Mean of sample mean = 245

d) Standard error of the mean = sd / sqrt(n) = 21 / sqrt(35) = 3.550

e) False. Because standard error is inversely proportional to square root of sample size.

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