Question

Assume that the length of time you need to wait to be seated at your favorite restaurant is normally distributed with mean of 25 minutes, and a standard deviation of 10 minutes. If the restaurant decides to give a discount to 10% of customers who wait the longest, what is the cutoff wait time (in minutes) to get the discount? (Please answer rounded to the nearest minute.

Answer 1

To find the cutoff wait time to get the discount, we need to find the value that separates the top 10% of wait times from the rest. In a normal distribution, this value is known as the z-score. We can use the z-score formula z = (x - mean) / standard deviation, where x is the cutoff wait time and mean is the mean wait time. Rounding to the nearest minute, the cutoff wait time is 38 minutes.

Step-by-step explanation:

To find the cutoff wait time to get the discount, we need to find the value that separates the top 10% of wait times from the rest. In a normal distribution, this value is known as the z-score. We can use the z-score formula z = (x - mean) / standard deviation, where x is the cutoff wait time and mean is the mean wait time. We want to find the z-score that corresponds to the 90th percentile, which is 1.28. Rearranging the formula, we have 1.28 = (x - 25) / 10. Solving for x gives us x = (1.28 * 10) + 25 = 37.8. Rounding to the nearest minute, the cutoff wait time is 38 minutes.