Answer:The empirical rule, also known as the 68-95-99.7 rule, is a guideline that applies to data sets that are approximately normally distributed. According to this rule:
- Approximately 68% of the data falls within one standard deviation of the mean.
- Approximately 95% of the data falls within two standard deviations of the mean.
- Approximately 99.7% of the data falls within three standard deviations of the mean.
In this case, we have a normal distribution with a mean of 32 minutes and a standard deviation of 2 minutes. To find the percentage of customers who have to wait between 26 minutes and 38 minutes, we can calculate the z-scores for each value and use the empirical rule.
The z-score is calculated by subtracting the mean from the given value and then dividing by the standard deviation. For 26 minutes:
z = (26 - 32) / 2 = -3
For 38 minutes:
z = (38 - 32) / 2 = 3
Now, we can refer to the empirical rule. Since the values are within three standard deviations of the mean, we know that approximately 99.7% of the data falls within this range.
Therefore, the percentage of customers who have to wait between 26 minutes and 38 minutes is approximately 99.7%.
Keep in mind that the empirical rule is an approximation and assumes a normal distribution. While it provides a useful guideline, it may not be perfectly accurate in all cases.
Step-by-step explanation: what i just said