Understanding Normal Distribution and Z-Scores

The video tutorial explains the concept of normal distribution, focusing on a variable x with a mean of 21 and a standard deviation of 7. It demonstrates how to calculate z-scores for specific x values and how to find x values from given z-scores. The tutorial uses a normal distribution curve to visually represent these calculations and concludes with a summary of the key points discussed.

What is the mean of the normally distributed variable x?

• 14

• 21

• 28

• 35

If the standard deviation is 7, what is the value of x that is one standard deviation to the right of the mean?

• 14

• 21

• 35

• 28

How do you calculate the z-score for a given value of x?

• Divide the mean by the value of x

• Multiply the mean by the standard deviation

• Subtract the mean from x and divide by the standard deviation

• Add the mean to the value of x

What is the z-score for x = 25?

• 0.57

• 1.00

• 1.14

• 0.75

For x = 13, what is the approximate z-score?

• -0.57

• -1.14

• -0.75

• -1.00

If a z-score is 1.6, what is the corresponding value of x?

• 21

• 28

• 35

• 32.2

What value of x corresponds to a z-score of -0.8?

• 18.2

• 15.4

• 21

• 25

How do you find the value of x from a given z-score?

• Multiply the z-score by the mean

• Add the z-score to the mean

• Add the mean to the product of the z-score and standard deviation

• Subtract the z-score from the mean

What does a z-score of zero indicate about the value of x?

• x is one standard deviation below the mean

• x is equal to the mean

• x is one standard deviation above the mean

• x is two standard deviations above the mean

What is the mean value of x if its z-score is zero?

• 14

• 35

• 28

• 21