Normal Distribution

Front

What is a normal distribution?

Back

A normal distribution is a continuous probability distribution characterized by a symmetric bell-shaped curve, where most of the observations cluster around the central peak and probabilities for values further away from the mean taper off equally in both directions.

Front

What are the mean and standard deviation in a normal distribution?

Back

The mean is the average of all data points, and the standard deviation measures the dispersion or spread of the data points around the mean.

Front

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

Back

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

Front

How do you calculate a z-score?

Back

A 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. A positive z-score indicates the value is above the mean, while a negative z-score indicates it is below the mean.

Front

What is the significance of the area under the normal curve?

Back

The area under the normal curve represents the probability of a random variable falling within a particular range of values.

Front

What is the relationship between z-scores and percentiles?

Back

Z-scores can be used to determine percentiles, which indicate the percentage of data points that fall below a particular value in a normal distribution.

Front

How do you find the x-value corresponding to a given z-score?

Back

To find the x-value, use the formula: X = μ + (z * σ), where μ is the mean, z is the z-score, and σ is the standard deviation.

Front

What is the standard normal distribution?

Back

The standard normal distribution is a special case of the normal distribution with a mean of 0 and a standard deviation of 1.

Front

How do you interpret a z-score of -1.43?

Back

A z-score of -1.43 indicates that the value is 1.43 standard deviations below the mean.