Q7. Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.

Background

Topic: Standard Normal Distribution

This question tests your ability to find the probability (area) under the standard normal curve between two z-scores. The shaded region represents the probability that a randomly selected value falls between z = -1.13 and z = 1.13.

Key Terms and Formulas

• Standard normal distribution: A normal distribution with mean and standard deviation .

• z-score: The number of standard deviations a value is from the mean.

• Area under the curve: Represents probability for a range of z-scores.

• To find the area between two z-scores, use:

Step-by-Step Guidance

1. Identify the z-scores that bound the shaded region: and .

2. Use the standard normal table (or calculator) to find the area to the left of , denoted .

3. Find the area to the left of , denoted .

4. Subtract the area to the left of from the area to the left of to get the probability between these z-scores: .

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Q8. Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. Shaded area is 0.9599.

Background

Topic: Standard Normal Distribution Percentiles

This question tests your ability to find the z-score corresponding to a given cumulative probability (area to the left). The shaded area represents the probability that a randomly selected value is less than a certain z-score.

Key Terms and Formulas

• Percentile: The value below which a given percentage of observations fall.

• z-score: The number of standard deviations a value is from the mean.

• To find the z-score for a given area, use the standard normal table in reverse: Find the z-score where .

Step-by-Step Guidance

1. Recognize that the shaded area to the left of the unknown z-score is 0.9599.

2. Use the standard normal table to look up the z-score that corresponds to a cumulative probability of 0.9599.

3. Find the z-score value where .

4. Check the table for the closest value to 0.9599 and identify the corresponding z-score.

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Q14. Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.

Background

Topic: Standard Normal Distribution (Right Tail Probability)

This question tests your ability to find the probability (area) under the standard normal curve to the right of a given z-score. The shaded region represents the probability that a randomly selected value is greater than z = 0.59.

Key Terms and Formulas

• Standard normal distribution: A normal distribution with mean and standard deviation .

• z-score: The number of standard deviations a value is from the mean.

• Right tail probability:

Step-by-Step Guidance

1. Identify the z-score that bounds the shaded region: .

2. Use the standard normal table to find the area to the left of , denoted .

3. Subtract this area from 1 to find the area to the right: .

4. Set up the calculation for the right tail probability using the values from the table.

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