Understanding Z-Scores and Normal Distribution

This video tutorial explains how to find a specific data value given a probability under a normal distribution curve. It uses a practical example of determining the minimum test score required to qualify for an interview, given that only the top 10% of applicants are considered. The video walks through using a z-score table to find the probability and then applying the z-score formula to calculate the test score. The process is explained step-by-step, making it easy to understand and apply.

What is the main focus of the video tutorial?

• Finding a specific data value given a probability

• Calculating the standard deviation

• Finding the mean of a data set

• Understanding the concept of variance

In the hiring scenario, what percentage of applicants does the company want to interview?

• Top 10%

• Top 25%

• Top 5%

• Top 20%

What are the mean and standard deviation of the test scores in the hiring scenario?

• Mean: 120, Standard Deviation: 12

• Mean: 110, Standard Deviation: 15

• Mean: 130, Standard Deviation: 20

• Mean: 100, Standard Deviation: 10

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

• To determine the probability of a specific score

• To calculate the standard deviation

• To find the mean of the data set

• To find the area under the curve to the left of a z-score

How do you find the area to the right of a z-score using the z-score table?

• Divide the table value by 2

• Add 0.10 to the table value

• Subtract the table value from 1

• Multiply the table value by 2

What is the closest value to 0.90 found in the z-score table?

• 0.8990

• 0.8995

• 0.9000

• 0.8997

What z-score corresponds to the closest value to 0.90 in the z-score table?

• 1.28

• 1.25

• 1.35

• 1.30

What is the total area under a normal distribution curve?

• 1.5

• 1

• 2

• 0.5

What does the z-score table provide?

• The area to the right of a z-score

• The area to the left of a z-score

• The standard deviation of the distribution

• The mean of the distribution

What is the formula for calculating a z-score?

• z = (x - mean) / standard deviation

• z = (mean - x) / standard deviation

• z = (x + mean) / standard deviation

• z = (x * mean) / standard deviation