Could you please solve the problem below? I need detailed mathematical process steps and explanation. 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 $17\mathrm{.}08$ ppm and a standard deviation of $4\mathrm{.}5$ ppm$.$ Suppose that you draw a random sample of $12$ 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 $17\mathrm{.}18$ 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$)?$

Part ii$)$ Use normal approximation to find the probability that more than $44\mathrm{.}9\%$ of the sampled printers operate at the advertised speed $($i$.$e$.$ the printing speed is equal to or greater than $18$ ppm$)$

A$.0\mathrm{.}5070$

B$.0\mathrm{.}5834$

C$.0\mathrm{.}4930$

D$.0\mathrm{.}4166$