Final answer:
Using the empirical rule, approximately 99.7% of the ice cream amounts will fall within three standard deviations from the mean. Multiplying 99.7% by 800 uses yields 798.4, which we round down to 798, making option A the correct answer.
Step-by-step explanation:
The amount of ice cream dispensed from a machine that is normally distributed can be analyzed using the empirical rule. This rule states that approximately 68% of the data falls within one standard deviation of the mean, about 95% falls within two standard deviations, and about 99.7% falls within three standard deviations. Given that the machine is used 800 times in a day, we can expect that the number of times the machine dispenses an amount within three standard deviations from the mean would be approximately 99.7% of 800.
To calculate this, we take 0.997 times 800:
0.997 × 800 = 798.4
Since the number of times must be an integer, we would round down to 798. Therefore, the correct answer is option A, which states 798 times.