Understanding Normal Distribution and Z-scores

The video tutorial explains how to use the normal distribution and the empirical rule to determine the percentage of daily lightbulb replacement requests at a university. It covers the calculation of standard deviations from the mean and the use of Z-scores to find probabilities. The tutorial demonstrates the application of the 68-95-99.7 rule and provides a step-by-step guide to calculating the percentage of requests between specific values using both the empirical rule and Z-scores.

What is the mean number of daily lightbulb replacement requests at the university?

• 33

• 11

• 49

• 16

What is the standard deviation of the daily lightbulb replacement requests?

• 11

• 33

• 49

• 16

According to the empirical rule, what percentage of data falls within one standard deviation of the mean?

• 68%

• 95%

• 99.7%

• 34%

How many standard deviations below the mean is the value 16?

• 4

• 3

• 2

• 1

What is the approximate percentage of requests between 16 and 49?

• 95%

• 68%

• 49.85%

• 34%

What does a Z-score represent in a normal distribution?

• The range of the data

• The median of the data

• The number of standard deviations a value is from the mean

• The mean of the data

What is the Z-score for the value 16?

• -3

• -2

• -1

• 0

What is the Z-score for the mean value of 49?

• -1

• 1

• 0

• 3

In a standard normal distribution, what is the mean value?

• -1

• 1

• 0

• 49

What is the standard deviation in a standard normal distribution?

• 49

• 11

• 1

• 0