Intro to Normal Distribution

Front

What is the Empirical Rule in statistics?

Back

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

Front

What percentage of data falls within 1 standard deviation of the mean in a normal distribution?

Back

68%.

Front

What percentage of data falls within 2 standard deviations of the mean in a normal distribution?

Back

95%.

Front

What percentage of data falls within 3 standard deviations of the mean in a normal distribution?

Back

99.7%.

Front

Define mean in statistics.

Back

The mean is the average of a set of numbers, calculated by adding all the values together and dividing by the number of values.

Front

Define standard deviation.

Back

Standard deviation is a measure of the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values tend to be close to the mean, while a high standard deviation indicates that the values are spread out over a wider range.

Front

If a normal distribution has a mean of 50 and a standard deviation of 5, what is the z-score for a value of 60?

Back

The z-score is 2. (Calculated as (60 - 50) / 5 = 2).

Front

What is a z-score?

Back

A z-score indicates how many standard deviations an element is from the mean. It is calculated by subtracting the mean from the value and dividing by the standard deviation.

Front

In a normal distribution, what is the probability of a value being less than the mean?

Back

50%.

Front

What is the significance of the area under the normal distribution curve?

Back

The area under the curve represents the total probability of all outcomes, which equals 1 (or 100%).