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. It is defined by its mean (μ) and standard deviation (σ).

Front

What percentage of data falls within one standard deviation of the mean in a normal distribution?

Back

Approximately 68% of the data falls within one standard deviation (σ) of the mean (μ) in a normal distribution.

Front

What percentage of data falls within two standard deviations of the mean in a normal distribution?

Back

Approximately 95% of the data falls within two standard deviations (2σ) of the mean (μ) in a normal distribution.

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What percentage of data falls within three standard deviations of the mean in a normal distribution?

Back

Approximately 99.7% of the data falls within three standard deviations (3σ) of the mean (μ) 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 is the significance of the z-score in a normal distribution?

Back

The z-score indicates how many standard deviations a data point is from the mean. It helps in determining the probability of a value occurring within a normal distribution.

Front

If the mean waist size is 29 inches and the standard deviation is 1.4 inches, what is the z-score for a waist size of 31 inches?

Back

The z-score for a waist size of 31 inches is calculated as: z = (31 - 29) / 1.4 = 1.43.

Front

What is the empirical rule in statistics?

Back

The empirical rule states that for a normal distribution: 68% of data falls within 1σ, 95% within 2σ, and 99.7% within 3σ of the mean.

Front

How do you find the area under the normal curve for a given z-score?

Back

The area under the normal curve for a given z-score can be found using z-tables or statistical software, which provide the cumulative probability associated with that z-score.

Front

What is the mean and standard deviation of the heights of male students given as 1.7 m and 0.2 m?

Back

The mean height is 1.7 m and the standard deviation is 0.2 m.