Exploring Adding and Subtracting Rational Expressions

The video tutorial explains the concept of normal distribution using a bell curve, highlighting how data is distributed around the mean with standard deviations. It provides an example using statistics midterm scores to illustrate the application of normal distribution. The tutorial also covers the concept of z-scores, explaining how to calculate them and interpret their meaning in relation to the bell curve. Finally, it demonstrates calculating z-scores for specific test scores, reinforcing the understanding of data distribution and standard deviations.

What shape is commonly used to represent a normal distribution?

• Circle

• Square

• Bell curve

• Triangle

Approximately what percentage of data falls within one standard deviation from the mean in a normal distribution?

• 50%

• 99%

• 95%

• 68%

How much data is expected to fall within two standard deviations of the mean?

• 50%

• 68%

• 95%

• 99%

What percentage of data falls between 76 and 86 in the given example of midterm grades?

• 99%

• 50%

• 68%

• 95%

What is the range of grades that falls within two standard deviations from the mean in the example?

• 81 to 91

• 66 to 96

• 76 to 86

• 71 to 91

What does a z-score indicate?

• Total number of data points

• Average value of the dataset

• Median of the dataset

• Number of standard deviations a value is from the mean

Calculate the z-score for a data value of 83 with a mean of 81 and a standard deviation of 5.

• 1.0

• 0.4

• -0.4

• 2.0

If a student's z-score on a test is -0.75 and the mean score is 85 with a standard deviation of 4, what is the student's test score?

• 90

• 82

• 85

• 88

What test score corresponds to a z-score of 3, given a mean of 85 and a standard deviation of 4?

• 97

• 100

• 85

• 82

A z-score of 1.25 would predict a test score of what, if the mean is 85 and the standard deviation is 4?

• 90

• 85

• 95

• 100