Threshold for low percentile | Modeling data distributions | AP Statistics | Khan Academy

TL;DR

Amelia wants to know the maximum average wait time for drive-through restaurants in her town that falls within the bottom 10% of wait times.

Transcript

• [Instructor] The distribution of average wait times in drive-through restaurant lines in one town was approximately normal with mean of 185 seconds and standard deviation of 11 seconds. Amelia only likes to use the drive-through for restaurants where the average wait time is in the bottom 10% for that town. What is the maximum average wait time f... Read More

Key Insights

• ⌛ The distribution of average wait times in drive-through restaurants in Amelia's town is approximately normal.
• ⌛ The mean wait time is 185 seconds, and the standard deviation is 11 seconds.
• 😒 Amelia wants to use the drive-through at restaurants with wait times in the bottom 10%.
• 🤪 By finding the z-score corresponding to the 10th percentile, we can determine the maximum average wait time.
• 🤪 The z-score is -1.29, indicating how many standard deviations below the mean the threshold value is.
• 🤪 Multiplying the z-score by the standard deviation and subtracting it from the mean gives us the threshold value.

Questions & Answers

Q: How is the distribution of average wait times in drive-through restaurants in Amelia's town described?

The distribution of average wait times in drive-through restaurants in Amelia's town is approximately normal, with a mean of 185 seconds and a standard deviation of 11 seconds.

Q: What is Amelia's requirement for using the drive-through at restaurants?

Amelia only wants to use the drive-through at restaurants where the average wait time is in the bottom 10% for her town.

Q: How can we determine the threshold value for the maximum average wait time Amelia is looking for?

The threshold value is the largest wait time for which Amelia is still within the bottom 10%. We can find this value by calculating the z-score that corresponds to the 10th percentile and converting it back to the actual wait time.

Q: What is the maximum average wait time for restaurants where Amelia likes to use the drive-through?

The maximum average wait time is approximately 170 or 171 seconds, rounded to the nearest whole second, based on Amelia's requirement to be within the bottom 10% of wait times.

Summary & Key Takeaways

• The distribution of average wait times in drive-through restaurant lines in Amelia's town follows an approximately normal distribution.

• The mean wait time is 185 seconds, with a standard deviation of 11 seconds.

• Amelia wants to know the maximum average wait time that falls within the bottom 10% of wait times.