An event, which takes place every three years on the first weekend in July in the city X$.$ The city X is evaluating the installation of portable toilets at an outdoor venue where the event is going to take place. In particular, it is considering an area of the venue that is far away from the existing restrooms. Assume there will be one single queue to access all the portable toilets in this area and that only one person uses a toilet at a time. City X is concerned that if the line is too long, people will find other ways and places to answer nature's call.

City X estimates that there will be $4$ arrivals per minute on average to the toilets, with a standard deviation of the time between arrivals of $15$ seconds. The average time a person spends using the toilet is $3\mathrm{.}25$ minutes with a standard deviation of $2$ minutes.

Question $1$:$$

Suppose city X installs $20$ portable toilets. On average, what fraction of the toilets will be occupied during the event?

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$($Please round your answer to two decimals. For instance, if the answer is $0\mathrm{.}312,$ then enter your answer as $0\mathrm{.}31)$

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Question $2$:

What is the minimum number of portable toilets that city X must install to ensure that the queue length will not continue to grow without limit $($i$.$e$.,$ so that the queue will be stable$)?($Note: Your answer should be an integer$$they can install $2$ toilets or $3$ toilets, but they cannot install $2\mathrm{.}6$ toilets.$)$ Please round up to the nearest integer.

$\_\_\_\_\_\_\_\_\_$toilet$($s$)$