Stats - 6.2 Online Homework

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 does the mean represent in a data set?

Back

The mean is the average of all data points in a set, calculated by adding all values and dividing by the number of values.

Front

What is standard deviation?

Back

Standard deviation is a measure of the amount of variation or dispersion in a set of values.

Front

How does the standard deviation affect the shape of a normal distribution?

Back

A smaller standard deviation results in a steeper curve, while a larger standard deviation results in a flatter curve.

Front

What is the empirical rule in statistics?

Back

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

Front

What does it mean if a data point is at the blue circle in a normal distribution graph?

Back

It indicates a specific value that is a certain number of standard deviations away from the mean.

Front

If the mean is 30 and the standard deviation is 5, what is the value at one standard deviation below the mean?

Back

25 (30 - 5).

Front

If the mean is 30 and the standard deviation is 5, what is the value at one standard deviation above the mean?

Back

35 (30 + 5).

Front

What is the z-score?

Back

The z-score indicates how many standard deviations a data point is from the mean.

Front

How do you calculate the z-score?

Back

Z-score = (X - mean) / standard deviation.