AP Statistics Flashcards: The Normal Distribution

What this deck covers

This deck focuses on The Normal Distribution, giving you a quick way to review the definitions, rules, and examples that matter most for AP Statistics.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: Identify the symmetry property of a normal distribution curve.

Answer: Symmetric about the mean. Normal curves are perfectly symmetric around their center.

Flashcard 2: What is the mode of a normal distribution with mean $\nu$?

Answer: $\nu$. Mode equals mean in normal distributions.

Flashcard 3: What is the median of a normal distribution with mean $\nu$?

Answer: $\nu$. Median equals mean due to symmetry.

Flashcard 4: State the property of normal distribution regarding mean and spread.

Answer: Mean determines center, standard deviation determines spread. Parameters control location and width of distribution.

Flashcard 5: What is the empirical rule in the context of normal distribution?

Answer: 68-95-99.7 rule. Also known as the three-sigma rule.

Flashcard 6: What property describes the tails of a normal distribution?

Answer: Asymptotic. Tails approach but never touch the x-axis.

Flashcard 7: What is the significance of the Central Limit Theorem in normal distribution?

Answer: Sample means are normally distributed. CLT ensures sampling distributions approach normality.

Flashcard 8: What does the Z-score represent in a normal distribution?

Answer: Number of standard deviations from the mean. Measures distance from mean in standard deviation units.

Flashcard 9: Determine the area to the left of $Z = 0$ in a standard normal distribution.

Answer: 0.5. Standard normal is symmetric around zero.

Flashcard 10: What is the mean of a standard normal distribution?

Answer:

1. Standard normal is centered at zero.

Flashcard 11: State the property of normal distribution regarding mean and spread.

Answer: Mean determines center, standard deviation determines spread. Parameters control location and width of distribution.

Flashcard 12: What is the median of a normal distribution with mean $\nu$?

Answer: $\nu$. Median equals mean due to symmetry.

Flashcard 13: What is the shape of a normal distribution curve?

Answer: Bell-shaped. Classic shape of normal distribution curves.

Flashcard 14: What is the relationship between variance and standard deviation?

Answer: Variance is the square of the standard deviation. Variance is standard deviation squared.

Flashcard 15: How are the mean, median, and mode related in a normal distribution?

Answer: They are equal. Symmetry ensures all central tendencies coincide.

Flashcard 16: Identify the symmetry property of a normal distribution curve.

Answer: Symmetric about the mean. Normal curves are perfectly symmetric around their center.

Flashcard 17: Find the probability $P(-1 < Z < 1)$ in a standard normal distribution.

Answer: 0.6826. 68% rule applied to standard normal.

Flashcard 18: What property describes the tails of a normal distribution?

Answer: Asymptotic. Tails approach but never touch the x-axis.

Flashcard 19: What is the skewness of a normal distribution?

Answer: 0 (perfectly symmetrical). No skew means perfectly balanced distribution.

Flashcard 20: How are the mean, median, and mode related in a normal distribution?

Answer: They are equal. Symmetry ensures all central tendencies coincide.

Flashcard 21: What is the total area under a normal distribution curve?

Answer:

1. Probability density functions always integrate to 1.

Flashcard 22: What is the standard deviation of a standard normal distribution?

Answer:

1. Standard normal has unit variance.

Flashcard 23: What is the purpose of normality tests in statistics?

Answer: Assess if data follows a normal distribution. Tests check if sample data appears normally distributed.

Flashcard 24: What is the mode of a normal distribution with mean $\nu$?

Answer: $\nu$. Mode equals mean in normal distributions.

Flashcard 25: What is the total area under a normal distribution curve?

Answer:

1. Probability density functions always integrate to 1.

Flashcard 26: Determine the area to the left of $Z = 0$ in a standard normal distribution.

Answer: 0.5. Standard normal is symmetric around zero.

Flashcard 27: What is the standard deviation of a standard normal distribution?

Answer:

1. Standard normal has unit variance.

Flashcard 28: What type of variable does a normal distribution model?

Answer: Continuous random variable. Normal distributions apply to continuous data only.

Flashcard 29: Determine the area to the right of $Z = 1.96$ in a standard normal distribution.

Answer: 0.025. Critical value leaving 2.5% in upper tail.

Flashcard 30: What is the purpose of normality tests in statistics?

Answer: Assess if data follows a normal distribution. Tests check if sample data appears normally distributed.

Flashcard 31: What percentage of data falls within one standard deviation of the mean in a normal distribution?

Answer: 68%. Empirical rule for one standard deviation interval.

Flashcard 32: What percentage of data falls within three standard deviations of the mean in a normal distribution?

Answer: 99.7%. Empirical rule for three standard deviation interval.

Flashcard 33: What does the Z-score represent in a normal distribution?

Answer: Number of standard deviations from the mean. Measures distance from mean in standard deviation units.

Flashcard 34: What is the skewness of a normal distribution?

Answer: 0 (perfectly symmetrical). No skew means perfectly balanced distribution.

Flashcard 35: Find the probability $P(-1 < Z < 1)$ in a standard normal distribution.

Answer: 0.6826. 68% rule applied to standard normal.

Flashcard 36: What percentage of data falls within two standard deviations of the mean in a normal distribution?

Answer: 95%. Empirical rule for two standard deviation interval.

Flashcard 37: What is the empirical rule in the context of normal distribution?

Answer: 68-95-99.7 rule. Also known as the three-sigma rule.

Flashcard 38: What is the mean of a standard normal distribution?

Answer:

1. Standard normal is centered at zero.

Flashcard 39: What percentage of data falls within two standard deviations of the mean in a normal distribution?

Answer: 95%. Empirical rule for two standard deviation interval.

Flashcard 40: What is the main use of the standard normal distribution table?

Answer: Find probabilities for Z-scores. Standard tables give cumulative probabilities for Z-values.

Flashcard 41: What is the shape of a normal distribution curve?

Answer: Bell-shaped. Classic shape of normal distribution curves.

Flashcard 42: What is the main use of the standard normal distribution table?

Answer: Find probabilities for Z-scores. Standard tables give cumulative probabilities for Z-values.

Flashcard 43: What is the relationship between variance and standard deviation?

Answer: Variance is the square of the standard deviation. Variance is standard deviation squared.

Flashcard 44: Determine the area to the right of $Z = 1.96$ in a standard normal distribution.

Answer: 0.025. Critical value leaving 2.5% in upper tail.

Flashcard 45: What percentage of data falls within three standard deviations of the mean in a normal distribution?

Answer: 99.7%. Empirical rule for three standard deviation interval.

Flashcard 46: What type of variable does a normal distribution model?

Answer: Continuous random variable. Normal distributions apply to continuous data only.

Flashcard 47: What is the significance of the Central Limit Theorem in normal distribution?

Answer: Sample means are normally distributed. CLT ensures sampling distributions approach normality.

Flashcard 48: What percentage of data falls within one standard deviation of the mean in a normal distribution?

Answer: 68%. Empirical rule for one standard deviation interval.