The Normal Distribution Practice

Front

What is the mean in a normal distribution?

Back

The mean is the average value of a set of data points, representing the center of the distribution.

Front

What is the standard deviation in a normal distribution?

Back

The standard deviation measures the amount of variation or dispersion in a set of values.

Front

What does it mean for data to be normally distributed?

Back

Data is normally distributed when it follows a bell-shaped curve, where most values cluster around the mean and probabilities for values further away from the mean taper off equally in both directions.

Front

What is the empirical rule (68-95-99.7 rule)?

Back

The empirical rule states that for a normal distribution: 68% of data falls within one standard deviation of the mean, 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 proportion of data falls below the mean in a normal distribution?

Back

50% of the data falls below the mean in a normal distribution.

Front

What is the significance of the top 2% in a normal distribution?

Back

The top 2% represents the threshold for the highest scores, often used for criteria like membership in organizations such as Mensa.

Front

How do you find the probability of a value in a normal distribution?

Back

To find the probability of a value, calculate the z-score and then use the standard normal distribution table to find the corresponding probability.

Front

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

Back

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

Front

What is the area under the curve in a normal distribution?

Back

The total area under the curve of a normal distribution is equal to 1, representing the total probability.