The Normal Distribution - AP Statistics
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What is the mode of a normal distribution with mean $\nu$?
What is the mode of a normal distribution with mean $\nu$?
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$\nu$. Mode equals mean in normal distributions.
$\nu$. Mode equals mean in normal distributions.
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What is the median of a normal distribution with mean $\nu$?
What is the median of a normal distribution with mean $\nu$?
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$\nu$. Median equals mean due to symmetry.
$\nu$. Median equals mean due to symmetry.
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Find the probability $P(-1 < Z < 1)$ in a standard normal distribution.
Find the probability $P(-1 < Z < 1)$ in a standard normal distribution.
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0.6826. 68% rule applied to standard normal.
0.6826. 68% rule applied to standard normal.
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What property describes the tails of a normal distribution?
What property describes the tails of a normal distribution?
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Asymptotic. Tails approach but never touch the x-axis.
Asymptotic. Tails approach but never touch the x-axis.
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What is the main use of the standard normal distribution table?
What is the main use of the standard normal distribution table?
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Find probabilities for Z-scores. Standard tables give cumulative probabilities for Z-values.
Find probabilities for Z-scores. Standard tables give cumulative probabilities for Z-values.
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How are the mean, median, and mode related in a normal distribution?
How are the mean, median, and mode related in a normal distribution?
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They are equal. Symmetry ensures all central tendencies coincide.
They are equal. Symmetry ensures all central tendencies coincide.
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What type of variable does a normal distribution model?
What type of variable does a normal distribution model?
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Continuous random variable. Normal distributions apply to continuous data only.
Continuous random variable. Normal distributions apply to continuous data only.
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What is the significance of the Central Limit Theorem in normal distribution?
What is the significance of the Central Limit Theorem in normal distribution?
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Sample means are normally distributed. CLT ensures sampling distributions approach normality.
Sample means are normally distributed. CLT ensures sampling distributions approach normality.
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What is the relationship between variance and standard deviation?
What is the relationship between variance and standard deviation?
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Variance is the square of the standard deviation. Variance is standard deviation squared.
Variance is the square of the standard deviation. Variance is standard deviation squared.
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What does the Z-score represent in a normal distribution?
What does the Z-score represent in a normal distribution?
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Number of standard deviations from the mean. Measures distance from mean in standard deviation units.
Number of standard deviations from the mean. Measures distance from mean in standard deviation units.
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Determine the area to the right of $Z = 1.96$ in a standard normal distribution.
Determine the area to the right of $Z = 1.96$ in a standard normal distribution.
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0.025. Critical value leaving 2.5% in upper tail.
0.025. Critical value leaving 2.5% in upper tail.
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What property describes the tails of a normal distribution?
What property describes the tails of a normal distribution?
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Asymptotic. Tails approach but never touch the x-axis.
Asymptotic. Tails approach but never touch the x-axis.
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Determine the area to the left of $Z = 0$ in a standard normal distribution.
Determine the area to the left of $Z = 0$ in a standard normal distribution.
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0.5. Standard normal is symmetric around zero.
0.5. Standard normal is symmetric around zero.
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State the property of normal distribution regarding mean and spread.
State the property of normal distribution regarding mean and spread.
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Mean determines center, standard deviation determines spread. Parameters control location and width of distribution.
Mean determines center, standard deviation determines spread. Parameters control location and width of distribution.
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What is the significance of the Central Limit Theorem in normal distribution?
What is the significance of the Central Limit Theorem in normal distribution?
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Sample means are normally distributed. CLT ensures sampling distributions approach normality.
Sample means are normally distributed. CLT ensures sampling distributions approach normality.
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What is the mean of a standard normal distribution?
What is the mean of a standard normal distribution?
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- Standard normal is centered at zero.
- Standard normal is centered at zero.
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What type of variable does a normal distribution model?
What type of variable does a normal distribution model?
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Continuous random variable. Normal distributions apply to continuous data only.
Continuous random variable. Normal distributions apply to continuous data only.
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What does the Z-score represent in a normal distribution?
What does the Z-score represent in a normal distribution?
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Number of standard deviations from the mean. Measures distance from mean in standard deviation units.
Number of standard deviations from the mean. Measures distance from mean in standard deviation units.
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What is the standard deviation of a standard normal distribution?
What is the standard deviation of a standard normal distribution?
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- Standard normal has unit variance.
- Standard normal has unit variance.
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Identify the symmetry property of a normal distribution curve.
Identify the symmetry property of a normal distribution curve.
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Symmetric about the mean. Normal curves are perfectly symmetric around their center.
Symmetric about the mean. Normal curves are perfectly symmetric around their center.
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What is the mode of a normal distribution with mean $\nu$?
What is the mode of a normal distribution with mean $\nu$?
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$\nu$. Mode equals mean in normal distributions.
$\nu$. Mode equals mean in normal distributions.
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What is the median of a normal distribution with mean $\nu$?
What is the median of a normal distribution with mean $\nu$?
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$\nu$. Median equals mean due to symmetry.
$\nu$. Median equals mean due to symmetry.
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What is the shape of a normal distribution curve?
What is the shape of a normal distribution curve?
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Bell-shaped. Classic shape of normal distribution curves.
Bell-shaped. Classic shape of normal distribution curves.
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What percentage of data falls within one standard deviation of the mean in a normal distribution?
What percentage of data falls within one standard deviation of the mean in a normal distribution?
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68%. Empirical rule for one standard deviation interval.
68%. Empirical rule for one standard deviation interval.
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What percentage of data falls within two standard deviations of the mean in a normal distribution?
What percentage of data falls within two standard deviations of the mean in a normal distribution?
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95%. Empirical rule for two standard deviation interval.
95%. Empirical rule for two standard deviation interval.
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What percentage of data falls within three standard deviations of the mean in a normal distribution?
What percentage of data falls within three standard deviations of the mean in a normal distribution?
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99.7%. Empirical rule for three standard deviation interval.
99.7%. Empirical rule for three standard deviation interval.
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What is the empirical rule in the context of normal distribution?
What is the empirical rule in the context of normal distribution?
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68-95-99.7 rule. Also known as the three-sigma rule.
68-95-99.7 rule. Also known as the three-sigma rule.
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What is the total area under a normal distribution curve?
What is the total area under a normal distribution curve?
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- Probability density functions always integrate to 1.
- Probability density functions always integrate to 1.
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Determine the area to the right of $Z = 1.96$ in a standard normal distribution.
Determine the area to the right of $Z = 1.96$ in a standard normal distribution.
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0.025. Critical value leaving 2.5% in upper tail.
0.025. Critical value leaving 2.5% in upper tail.
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Find the probability $P(-1 < Z < 1)$ in a standard normal distribution.
Find the probability $P(-1 < Z < 1)$ in a standard normal distribution.
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0.6826. 68% rule applied to standard normal.
0.6826. 68% rule applied to standard normal.
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