Normal Distribution Practice

Front

What is a normal distribution?

Back

A normal distribution is a continuous probability distribution characterized by a symmetric bell-shaped curve, where the mean, median, and mode are all equal.

Front

What is the mean in a normal distribution?

Back

The mean is the average of all data points in a normal distribution, representing the center of the distribution.

Front

What is the standard deviation in a normal distribution?

Back

The standard deviation measures the dispersion or spread of data points around the mean in a normal distribution.

Front

How do you calculate the z-score?

Back

The z-score is calculated using the formula: z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.

Front

What does a z-score represent?

Back

A z-score represents the number of standard deviations a data point is from the mean of the distribution.

Front

What is the significance of a z-score of 0?

Back

A z-score of 0 indicates that the data point is exactly at the mean of the distribution.

Front

What is the area under the normal curve?

Back

The total area under the normal curve is equal to 1, representing the total probability of all outcomes.

Front

What is the empirical rule (68-95-99.7 rule)?

Back

The empirical rule states that in a normal distribution, approximately 68% of data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.

Front

How do you find the probability of a z-score?

Back

To find the probability of a z-score, use the standard normal distribution table (z-table) to look up the area to the left of the z-score.

Front

What is the cutoff score for the top 10% in a normal distribution?

Back

To find the cutoff score for the top 10%, locate the z-score that corresponds to the 90th percentile and use the formula: x = μ + zσ.