AP Statistics Flashcards: Introducing Statistics Why Be Normal

What this deck covers

This deck focuses on Introducing Statistics Why Be Normal, 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: State the property of symmetry in a normal distribution.

Answer: Symmetrical about the mean. Equal areas on both sides of the mean create perfect symmetry.

Flashcard 2: Find the z-score for $x = 15$, given $\text{μ} = 15$ and $\text{σ} = 5$.

Answer:

1. Using $z = \frac{15-15}{5} = 0$.

Flashcard 3: What is the function used to standardize a normal variable?

Answer: $z = \frac{x - \text{μ}}{\text{σ}}$. Z-score formula converts any normal variable to standard normal.

Flashcard 4: What is a z-score?

Answer: Standard score indicating deviation from mean. Measures how many standard deviations a value is from the mean.

Flashcard 5: Find the area to the left of $z = -2$ in a standard normal distribution.

Answer: 0.0228. Standard normal table gives area left of $z = -2$.

Flashcard 6: What does the area under a normal distribution curve represent?

Answer: Probability. Area under any probability density curve represents probability.

Flashcard 7: Find the area between $z = -2$ and $z = 2$ in a standard normal distribution.

Answer: 0.9545. This represents 95% of the distribution within two standard deviations.

Flashcard 8: Find the area between $z = -2$ and $z = 2$ in a standard normal distribution.

Answer: 0.9545. This represents 95% of the distribution within two standard deviations.

Flashcard 9: Find the z-score for $x = 7$, $\text{μ} = 5$, $\text{σ} = 1$.

Answer:

1. Using $z = \frac{7-5}{1} = 2$.

Flashcard 10: What percentage of data falls within one standard deviation in a normal distribution?

Answer: 68%. First part of the 68-95-99.7 empirical rule.

Flashcard 11: Which z-score corresponds to the 5th percentile?

Answer: -1.645. Critical z-value that leaves 5% in the lower tail.

Flashcard 12: What is the relationship between mean, median, and mode in a normal distribution?

Answer: They are equal. Perfect symmetry makes all three measures of central tendency identical.

Flashcard 13: What does a z-score of 0 indicate?

Answer: Value equals the mean. Zero z-score means the observation equals the population mean.

Flashcard 14: Identify the empirical rule for normal distributions.

Answer: 68-95-99.7 rule. Also known as the empirical rule for normal distribution percentages.

Flashcard 15: What percentage of data falls within three standard deviations in a normal distribution?

Answer: 99.7%. Third part of the 68-95-99.7 empirical rule.

Flashcard 16: What is the function used to standardize a normal variable?

Answer: $z = \frac{x - \mu}{\sigma}$. Z-score formula converts any normal variable to standard normal.

Flashcard 17: What percentage of data falls within two standard deviations in a normal distribution?

Answer: 95%. Second part of the 68-95-99.7 empirical rule.

Flashcard 18: Find the area to the left of $z = 1$ in a standard normal distribution.

Answer: 0.8413. Standard normal table gives area left of $z = 1$.

Flashcard 19: Find the z-score for $x = 12$, given $\text{μ} = 10$ and $\text{σ} = 4$.

Answer: 0.5. Using $z = \frac{12-10}{4} = 0.5$.

Flashcard 20: State the property of symmetry in a normal distribution.

Answer: Symmetrical about the mean. Equal areas on both sides of the mean create perfect symmetry.

Flashcard 21: Find the probability of $z < -2$ in a standard normal distribution.

Answer: 0.0228. Standard normal table gives area left of $z = -2$.

Flashcard 22: Find the z-score for $x = 7$, $\text{μ} = 5$, $\text{σ} = 1$.

Answer:

1. Using $z = \frac{7-5}{1} = 2$.

Flashcard 23: Find the z-score for $x = 5$, given $\text{μ} = 3$ and $\text{σ} = 2$.

Answer:

1. Using $z = \frac{5-3}{2} = 1$.

Flashcard 24: What is the effect of increasing standard deviation on a normal curve?

Answer: Flattens and widens the curve. Larger σ spreads data more widely around the mean.

Flashcard 25: Find the area to the left of $z = -2$ in a standard normal distribution.

Answer: 0.0228. Standard normal table gives area left of $z = -2$.

Flashcard 26: Find the probability of $z < -2$ in a standard normal distribution.

Answer: 0.0228. Standard normal table gives area left of $z = -2$.

Flashcard 27: Find the z-score for $x = 12$, given $\text{μ} = 10$ and $\text{σ} = 4$.

Answer: 0.5. Using $z = \frac{12-10}{4} = 0.5$.

Flashcard 28: Find the area to the right of $z = -1$ in a standard normal distribution.

Answer: 0.8413. Area to the right of $z = -1$ equals area to the left of $z = 1$.

Flashcard 29: What is the probability that a z-score is exactly 0 in a continuous normal distribution?

Answer:

1. Continuous distributions assign zero probability to any single point.

Flashcard 30: Find the area to the right of $z = -1$ in a standard normal distribution.

Answer: 0.8413. Area to the right of $z = -1$ equals area to the left of $z = 1$.

Flashcard 31: What is the effect of decreasing standard deviation on a normal curve?

Answer: Narrows and steepens the curve. Smaller σ concentrates data more tightly around the mean.

Flashcard 32: What is the kurtosis of a normal distribution?

Answer:

1. Mesokurtic distribution with standard baseline kurtosis value.

Flashcard 33: How does a normal distribution relate to the Central Limit Theorem?

Answer: Sample means are normally distributed. CLT states that sample means approach normality regardless of population shape.

Flashcard 34: What percentage of data falls within three standard deviations in a normal distribution?

Answer: 99.7%. Third part of the 68-95-99.7 empirical rule.

Flashcard 35: What is the cumulative distribution function (CDF) used for?

Answer: To find probabilities. CDF gives probability that random variable is less than or equal to x.

Flashcard 36: Identify the range of the majority of data points in a normal distribution.

Answer: Within $\text{μ} \text{±} 3\text{σ}$. Three standard deviations captures 99.7% of all data points.

Flashcard 37: What percentage of data falls within one standard deviation in a normal distribution?

Answer: 68%. First part of the 68-95-99.7 empirical rule.

Flashcard 38: Identify the range of the majority of data points in a normal distribution.

Answer: Within $\mu \pm 3\sigma$. Three standard deviations captures 99.7% of all data points.

Flashcard 39: Identify the empirical rule for normal distributions.

Answer: 68-95-99.7 rule. Also known as the empirical rule for normal distribution percentages.

Flashcard 40: Identify the skewness of a normal distribution.

Answer: Zero. Perfect symmetry means no skewness in either direction.

Flashcard 41: Find the probability of $z > 2$ in a standard normal distribution.

Answer: 0.0228. Using $1 - 0.9772 = 0.0228$ from standard normal table.

Flashcard 42: What does a z-score of 0 indicate?

Answer: Value equals the mean. Zero z-score means the observation equals the population mean.

Flashcard 43: What is the relationship between mean, median, and mode in a normal distribution?

Answer: They are equal. Perfect symmetry makes all three measures of central tendency identical.

Flashcard 44: What is the cumulative distribution function (CDF) used for?

Answer: To find probabilities. CDF gives probability that random variable is less than or equal to x.

Flashcard 45: How does a normal distribution relate to the Central Limit Theorem?

Answer: Sample means are normally distributed. CLT states that sample means approach normality regardless of population shape.

Flashcard 46: Find the area to the left of $z = 1$ in a standard normal distribution.

Answer: 0.8413. Standard normal table gives area left of $z = 1$.

Flashcard 47: Which z-score corresponds to the 5th percentile?

Answer: -1.645. Critical z-value that leaves 5% in the lower tail.

Flashcard 48: Identify the skewness of a normal distribution.

Answer: Zero. Perfect symmetry means no skewness in either direction.

Flashcard 49: Calculate the z-score for $x = 10$, $\text{μ} = 8$, $\text{σ} = 1.5$.

Answer: 1.33. Using $z = \frac{10-8}{1.5} = 1.33$.

Flashcard 50: Identify the z-score for the mean in a standard normal distribution.

Answer:

1. The mean has zero deviation from itself by definition.

Flashcard 51: Find the area between $z = -1$ and $z = 1$ in a standard normal distribution.

Answer: 0.6826. This represents the middle 68% of the distribution.

Flashcard 52: What is the standard deviation of a standard normal distribution?

Answer:

1. Standard normal distribution has unit variance and standard deviation.

Flashcard 53: Find the z-score for $x = 5$, given $\text{μ} = 3$ and $\text{σ} = 2$.

Answer:

1. Using $z = \frac{5-3}{2} = 1$.

Flashcard 54: What is the notation for a normal distribution with mean $\text{μ}$ and standard deviation $\text{σ}$?

Answer: $N(\text{μ}, \text{σ})$. Standard notation where μ is mean and σ is standard deviation.

Flashcard 55: Why is the normal distribution important in statistics?

Answer: Many variables are approximately normal. Central Limit Theorem and many natural phenomena follow normal distributions.

Flashcard 56: What is the effect of increasing standard deviation on a normal curve?

Answer: Flattens and widens the curve. Larger σ spreads data more widely around the mean.

Flashcard 57: What is the notation for a normal distribution with mean $\text{μ}$ and standard deviation $\text{σ}$?

Answer: $N(\text{μ}, \text{σ})$. Standard notation where μ is mean and σ is standard deviation.

Flashcard 58: Find the z-score for $x = 15$, given $\text{μ} = 15$ and $\text{σ} = 5$.

Answer:

1. Using $z = \frac{15-15}{5} = 0$.

Flashcard 59: Which z-score corresponds to the 95th percentile?

Answer: 1.645. Critical z-value that leaves 5% in the upper tail.

Flashcard 60: What is the probability that a z-score is exactly 0 in a continuous normal distribution?

Answer:

1. Continuous distributions assign zero probability to any single point.

Flashcard 61: Find the probability of $z > 2$ in a standard normal distribution.

Answer: 0.0228. Using $1 - 0.9772 = 0.0228$ from standard normal table.

Flashcard 62: Identify the z-score for the mean in a standard normal distribution.

Answer:

1. The mean has zero deviation from itself by definition.

Flashcard 63: What is the shape of a normal distribution curve?

Answer: Bell-shaped. The normal curve resembles a bell due to its symmetric, unimodal shape.

Flashcard 64: What is the effect of decreasing standard deviation on a normal curve?

Answer: Narrows and steepens the curve. Smaller σ concentrates data more tightly around the mean.

Flashcard 65: Find the area between $z = -1$ and $z = 1$ in a standard normal distribution.

Answer: 0.6826. This represents the middle 68% of the distribution.

Flashcard 66: Why is the normal distribution important in statistics?

Answer: Many variables are approximately normal. Central Limit Theorem and many natural phenomena follow normal distributions.

Flashcard 67: What is the kurtosis of a normal distribution?

Answer:

1. Mesokurtic distribution with standard baseline kurtosis value.

Flashcard 68: What is the key characteristic of a normal distribution's tails?

Answer: Asymptotic. Tails approach but never touch the horizontal axis.

Flashcard 69: What is the key characteristic of a normal distribution's tails?

Answer: Asymptotic. Tails approach but never touch the horizontal axis.

Flashcard 70: Which z-score corresponds to the 95th percentile?

Answer: 1.645. Critical z-value that leaves 5% in the upper tail.

Flashcard 71: What does the area under a normal distribution curve represent?

Answer: Probability. Area under any probability density curve represents probability.

Flashcard 72: What is the mean of a standard normal distribution?

Answer:

1. Standard normal distribution is centered at zero by definition.

Flashcard 73: Calculate the z-score for $x = 10$, $\text{μ} = 8$, $\text{σ} = 1.5$.

Answer: 1.33. Using $z = \frac{10-8}{1.5} = 1.33$.

Flashcard 74: What percentage of data falls within two standard deviations in a normal distribution?

Answer: 95%. Second part of the 68-95-99.7 empirical rule.