Normal Distribution Concepts and 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 are the parameters of a normal distribution?

Back

The parameters of a normal distribution are the mean (μ) and the standard deviation (σ).

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 does a z-score represent?

Back

A z-score represents the number of standard deviations a data point is from the mean. A positive z-score indicates a value above the mean, while a negative z-score indicates a value below the mean.

Front

What is the significance of the mean in a normal distribution?

Back

The mean is the central point of a normal distribution and is the point around which the data is symmetrically distributed.

Front

What is the significance of the standard deviation in a normal distribution?

Back

The standard deviation measures the spread or dispersion of the data points around the mean in a normal distribution.

Front

If the mean life of a tire is 30,000 km and the standard deviation is 2000 km, what is the range for 68% of tires?

Back

28,000 km to 32,000 km.

Front

What is the probability of a value falling below the mean in a normal distribution?

Back

In a normal distribution, the probability of a value falling below the mean is 50%.

Front

What is the mean of the sampling distribution?

Back

The mean of the sampling distribution is equal to the mean of the population from which the samples are drawn.