(5-8) Normal Distribution portion of Algebra 2 final exam

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 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 of the data points from the mean.

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 of -2 indicate?

Back

A z-score of -2 indicates that the value is 2 standard deviations below the mean.

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 of the mean.

Front

What percentage of data falls above 2 standard deviations from the mean?

Back

About 2.5% of the data falls above 2 standard deviations from the mean.

Front

If the mean is 75 and the standard deviation is 7, what is the score at the 84th percentile?

Back

The score at the 84th percentile is approximately 82 (mean + 1 standard deviation).

Front

What is the empirical rule in statistics?

Back

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

Front

What is the significance of the standard deviation in a normal distribution?

Back

The standard deviation indicates how spread out the values are in a data set; a smaller standard deviation means values are closer to the mean.