Final answer:
The nurse should set the infusion pump to a rate of 62.5 milliliters/hour to administer 500 ml of dextrose 5% in normal saline solution over 8 hours.
Step-by-step explanation:
To determine the rate at which the nurse should set the infusion pump for the 3-year-old child to receive 500 ml of dextrose 5% in normal saline solution, we will calculate the flow rate in milliliters per hour (ml/hour). Given that the total volume to be infused is 500 ml and the time period is 8 hours:
Flow rate (ml/hour) = Total Volume (ml) / Total Time (hours)
Flow rate (ml/hour) = 500 ml / 8 hours
Flow rate (ml/hour) = 62.5 ml/hour
Therefore, the infusion pump should be set to a rate of 62.5 milliliters/hour, which is the amount of solution to be delivered each hour to complete the infusion over the prescribed 8 hours.