Understanding Normal Distribution and Z-Scores

The video tutorial explains how to determine the maximum average wait time for drive-thru restaurants that Amelia prefers, using the concept of normal distribution. It covers the calculation of the 10th percentile using a z-table and explains how to apply the z-score to find the desired wait time, rounding the result to the nearest whole second.

What is the mean wait time for drive-thru restaurants in the town?

• 185 seconds

• 205 seconds

• 195 seconds

• 175 seconds

What is the standard deviation of the wait times in the town?

• 9 seconds

• 11 seconds

• 12 seconds

• 10 seconds

What does a normal distribution imply about the data?

• Data is skewed to the left

• Data is evenly distributed around the mean

• Data is skewed to the right

• Data has multiple peaks

Tags

CCSS.HSS.ID.A.4

What is the significance of the dotted lines in the normal distribution visualization?

• They represent the mean

• They represent standard deviations from the mean

• They represent the mode

• They represent the median

What is the purpose of finding a z-score in this context?

• To calculate the mean

• To identify the maximum wait time for the bottom 10%

• To determine the standard deviation

• To find the average wait time

What does a z-score of -1.29 indicate?

• The wait time is exactly at the mean

• The wait time is above the mean

• The wait time is below the mean

• The wait time is in the top 10%

Tags

CCSS.HSS.ID.A.4

How do you calculate the actual wait time using the z-score?

• Add the z-score to the mean

• Subtract the z-score from the mean

• Multiply the z-score by the standard deviation and subtract from the mean

• Multiply the z-score by the standard deviation and add to the mean

What is the calculated wait time before rounding?

• 170.81 seconds

• 171.81 seconds

• 172.81 seconds

• 173.81 seconds

Tags

CCSS.HSS.ID.A.4

Why might you choose to round down to 170 seconds?

• To avoid crossing the 50th percentile

• To make calculations easier

• To ensure the wait time is in the bottom 10%

• To ensure the wait time is in the top 10%

Tags

CCSS.7.SP.A.2

What is the final rounded wait time that meets Amelia's needs?

• 171 seconds

• 170 seconds

• 172 seconds

• 169 seconds

Tags

CCSS.7.SP.A.2