Question

The wait times for a table at a popular Gastropub during peak hours are normally distributed, with the mean of 15 minutes. 68% of the wait times are between 12 and 18 minutes. What is the standard deviation of the response times in minutes?

Answer 1

The standard deviation of the response times in minutes is 3.

Step-by-step explanation:

The question is asking for the standard deviation of the response times in minutes for the wait times at a popular Gastropub during peak hours. We are given that the wait times are normally distributed and that 68% of the wait times are between 12 and 18 minutes. To find the standard deviation, we can use the properties of the normal distribution:

1. 68% of the data falls within one standard deviation of the mean.
2. For a normal distribution, the area under the curve between the mean minus one standard deviation and the mean plus one standard deviation is approximately 68%.
3. Therefore, the range from 12 to 18 minutes represents one standard deviation.
4. So the standard deviation is half of the range, which is (18-12)/2 = 3 minutes.

Therefore, the standard deviation of the response times in minutes is 3.