Normal Distributions

Front

What percentage of data falls within 1 standard deviation in a normal distribution according to the empirical rule?

Back

68%

Front

What percentage of golfers are between 30 and 46 years old if the ages are normally distributed with a mean of 38 and a standard deviation of 4?

Back

95%

Front

What does the center of a normal distribution curve represent?

Back

μ (mean)

Front

What percentage of students have a GPA between 2.9 and 3.8 if the mean GPA is 3.2 and the standard deviation is 0.3?

Back

81.5%

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

Front

Define standard deviation in the context of normal distributions.

Back

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

Front

What is the significance of the mean (μ) in a normal distribution?

Back

The mean (μ) is the average value and the center of the normal distribution curve.

Front

How do you calculate the z-score for a value in a normal distribution?

Back

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 indicate in a normal distribution?

Back

A z-score indicates how many standard deviations an element is from the mean.

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

Z = (60 - 50) / 5 = 2.