Calculating Areas with Z-Scores and Standard Normal Distribution

What is the mean and standard deviation of the standard normal distribution?

• Mean of 0 and standard deviation of 0

• Mean of 1 and standard deviation of 0

• Mean of 0 and standard deviation of 1

• Mean of 1 and standard deviation of 1

A z-score of -2 indicates that the observation is how many standard deviations from the mean?

• 1 standard deviation to the right

• 2 standard deviations to the left

• 1 standard deviation to the left

• 2 standard deviations to the right

What does the z-score table provide?

• The total area to the right of any z-score

• The total area to the left of any z-score

• The total area under the curve

• The total area above the curve

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

• Multiply the area to the left by 2

• Divide the area to the left by 2

• Subtract the area to the left from 1

• Add 1 to the area to the left

What is the area to the left of a z-score of 0.57 according to the z-score table?

• 0.4285

• 0.5715

• 0.2843

• 0.7157

How can you use the z-score table to find the z-score for a specific area?

• Look up the area in the table and find the corresponding z-score

• Divide the area by the standard deviation

• Multiply the area by the mean

• Subtract the area from 1

What is the benefit of standardization?

• It allows the use of the z-score table for any normal distribution

• It eliminates the need for a z-score table

• It changes the mean and standard deviation of the distribution

• It makes the distribution skewed

What is the formula for calculating a z-score?

• (X + μ) / σ

• (X - μ) / σ

• (X - σ) / μ

• (X + σ) / μ

If a chemistry exam has a mean score of 60 and a standard deviation of 10, what is the z-score for a score of 50?

• -1

• 1

• -2

• 0

In a normally distributed population with a mean height of 5.5 feet and a standard deviation of 0.5 feet, what is the z-score for a height of 6.3 feet?

• 0.62

• -0.62

• -1.6

• 1.6