To calculate the average time a customer will spend in the queue, we need to consider two factors: the arrival rate of customers and the service rate. The arrival rate of customers is given as $1$ customer per $4$ seconds, with a standard deviation of $5$ seconds. The service rate is given as $1$ customer per $2$ seconds, with a standard deviation of $4\mathrm{.}2$ seconds. To find the average time a customer will spend in the queue, we can use the following formula: Average time in queue $=($arrival rate $/$ service rate$)*($standard deviation of arrival rate $/$ standard deviation of service rate$)$ Plugging in the given values, we get: Average time in queue $=(1/2)*(5/4\mathrm{.}2)$ Average time in queue $0\mathrm{.}238$ seconds Therefore, the average time a customer will spend in the queue is approximately $0\mathrm{.}238$ seconds. To calculate the average time a customer will spend in the queue, we need to consider two factors: the arrival rate of customers and the service rate. The arrival rate of customers is given as $1$ customer per $4$ seconds, with a standard deviation of $5$ seconds. This means that customers arrive at a rate of $1/4$ per second, with some variation due to the standard deviation. The service rate is given as $1$ customer per $2$ seconds, with a standard deviation of $4\mathrm{.}2$ seconds. This means that services are provided at a rate of $1/2$ per second, also with some variation due to the standard deviation. To find the average time a customer will spend in the queue, we can use the following formula: Average time in queue $=($arrival rate $/$ service rate$)*($standard deviation of arrival rate $/$ standard deviation of service rate$)$ Plugging in the given values, we get: Average time in queue $=(1/2)*(5/4\mathrm{.}2)$ Average time in queue $0\mathrm{.}238$ seconds Therefore, the average time a customer will spend in the queue is approximately $0\mathrm{.}238$ seconds. This means that, on average, a customer will be in the queue for about $0\mathrm{.}238$ seconds before being served. Final answer: The average time a customer will spend in the queue $($in seconds$)$ is approximately $0\mathrm{.}238$ seconds.