Standard Normal Distribution

Front

What is a standard normal distribution?

Back

A standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1.

Front

What does a negative z-score indicate?

Back

A negative z-score indicates that the data value is below the mean.

Front

What does a positive z-score indicate?

Back

A positive z-score indicates that the data value is above the mean.

Front

How is a z-score calculated?

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 is the significance of a z-score of 0?

Back

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

Front

What is the area under the standard normal curve?

Back

The total area under the standard normal curve is equal to 1.

Front

What does the probability associated with a z-score represent?

Back

The probability associated with a z-score represents the area under the curve to the left of that z-score.

Front

What is the probability for a z-score of -2.0?

Back

The probability for a z-score of -2.0 is 0.0228.

Front

Which z-score corresponds to a probability of 0.3085?

Back

The z-score that corresponds to a probability of 0.3085 is -0.4.

Front

What is the empirical rule in relation to standard deviations?

Back

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