An HP 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 $17\mathrm{.}13$ ppm and a standard deviation of $4\mathrm{.}25$ ppm$.$ Suppose that you draw a random sample of $11$ printers.

Part i$)$ Using the information about the distribution of the printing speeds given by the manufacturer, find the probability that the mean printing speed of the sample is greater than $18\mathrm{.}03$ ppm$.($Please carry answers to at least six decimal places in intermediate steps. Give your final answer to the nearest three decimal places$).$

Probability $($as a proportion$)$