8.2 Normal Distribution Applications

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 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 in a normal distribution.

Front

What is the empirical rule in statistics?

Back

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

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

If the mean is 40 and the standard deviation is 10, what is the z-score for a score of 37?

Back

z = (37 - 40) / 10 = -0.3.

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.

Front

What is the mean and standard deviation of 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 find the proportion of data above a certain value in a normal distribution?

Back

To find the proportion of data above a certain value, calculate the z-score for that value and then use the standard normal distribution table.

Front

What is the relationship between mean, median, and mode in a normal distribution?

Back

In a normal distribution, the mean, median, and mode are all equal.