Final answer:
The correct answer is c. Approximately 99.7% of observations will fall within 90-150 seconds, according to the empirical rule, because the question refers to a normal distribution with a mean of 120 seconds and a standard deviation of 10 seconds.
Step-by-step explanation:
The question pertains to the empirical rule, which applies to symmetric, bell-shaped (normal) distributions. According to the empirical rule:
- Approximately 68% of observations will fall within 1 standard deviation of the mean.
- Approximately 95% of observations will fall within 2 standard deviations of the mean.
- Approximately 99.7% of observations will fall within 3 standard deviations of the mean.
Since the average time (mean) to fill orders at the drive-up window is 120 seconds and the standard deviation is 10 seconds:
- 68% of the observations will fall between 110 (120-10) and 130 (120+10) seconds.
- 95% of the observations will be between 100 (120-2×10) and 140 (120+2×10) seconds.
- 99.7% of the observations will fall between 90 (120-3×10) and 150 (120+3×10) seconds.
Thus, each statement reflects one of these three rules. The correct statement addressing the student's question using the empirical rule and the data provided would be:
- a. Approximately 68% of observations will fall within 110-130 seconds.
- b. Approximately 95% of observations will fall within 100-140 seconds.
- c. Approximately 99.7% of observations will fall within 90-150 seconds.
Since no statement is given regarding 99.7% of observations falling within 110-130 seconds, statement d is incorrect. Therefore, the correct answer to the student's question is c. Approximately 99.7% of observations will fall within 90-150 seconds.