A laser printer is advertised to print text documents at a speed of 18 ppm (pages per minute). The manufacturer tells you that the printing speed is actually a Normal random variable with a mean of 17.83 ppm and a standard deviation of 3.5 ppm.

i)Find the mean and standard deviation of the sampling distribution of sample means with sample sizen=31.

X=------------------

X=------------------------------

ii)Suppose that we draw a random sample of31 printers. Find the probability that the mean of our sample will be greater than18.23ppm.

Probability =------------------

iii)Suppose that we found all possible sample means for a sample of size31. Find the values that approximately95%of the sample means would fall between.

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Give probabilities in four decimal places and all other answers to at least two decimal places where applicable.