Understanding Normal Distribution and the Empirical Rule

The video tutorial explains how to use the empirical rule to analyze a normally distributed set of exam scores. It covers calculating the number of students scoring above the mean, within one and two standard deviations, and below certain thresholds. The tutorial emphasizes understanding the distribution's symmetry and applying percentage calculations to determine student performance across different score ranges.

What is the mean score of the exam scores distribution?

• 90

• 84

• 78

• 72

How many students scored higher than the mean score of 78?

• 700

• 800

• 750

• 650

What percentage of students scored between 72 and 84?

• 50%

• 68%

• 75%

• 80%

How many students scored between 66 and 90?

• 1200

• 1150

• 1235

• 1300

What percentage of students scored between the mean and one standard deviation above it?

• 50%

• 68%

• 34%

• 16%

How many students scored lower than 72?

• 400

• 500

• 208

• 300

What is the percentage of students scoring below 72?

• 20%

• 16%

• 10%

• 25%

What is the empirical rule's limitation mentioned in the video?

• It only accounts for 85% of the data

• It only accounts for 90% of the data

• It only accounts for 99.7% of the data

• It only accounts for 95% of the data

How many students scored below 84?

• 1092

• 1150

• 1050

• 1000

What percentage of students scored less than 84?

• 84%

• 70%

• 75%

• 80%