Finding Areas in Normal Distributions

Front

What is a normal distribution?

Back

A normal distribution is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

Front

What are the key parameters of a normal distribution?

Back

The key parameters are the mean (average) and the standard deviation (which measures the spread of the 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.

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 1 standard deviation, 95% within 2 standard deviations, and 99.7% within 3 standard deviations of the mean.

Front

How do you find the area under the normal curve?

Back

The area under the normal curve can be found using z-scores and standard normal distribution tables or calculators.

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What is the significance of the area to the left of a z-score?

Back

The area to the left of a z-score represents the proportion of the data that falls below that z-score.

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What is the significance of the area to the right of a z-score?

Back

The area to the right of a z-score represents the proportion of the data that falls above that z-score.

Front

How do you interpret a z-score of 1.5?

Back

A z-score of 1.5 indicates that the value is 1.5 standard deviations above the mean.

Front

What is the cumulative distribution function (CDF)?

Back

The CDF of a normal distribution gives the probability that a random variable is less than or equal to a certain value.