Warm-Up Normal Distribution

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 mean and standard deviation in a normal distribution?

Back

The mean is the average of all data points, while the standard deviation measures the dispersion of the data points from the mean.

Front

What does the empirical rule state about normal distributions?

Back

The empirical rule states that 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

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

Back

The area under the normal distribution curve represents the total probability of all outcomes, which equals 1.

Front

What percentage of data falls between the mean and one standard deviation above the mean in a normal distribution?

Back

Approximately 34% of the data falls between the mean and one standard deviation above the mean.

Front

What is the mean of a normally distributed dataset with a mean of 43 and a standard deviation of 14?

Back

The mean is 43.

Front

If a lightbulb has a mean life of 500 hours and a standard deviation of 100 hours, what is the expected number of lightbulbs lasting between 400 and 700 hours?

Back

Approximately 4075 lightbulbs.

Front

What does it mean if a data point is one standard deviation above the mean?

Back

It means the data point is greater than the mean by an amount equal to the standard deviation.

Front

What is the range in a normal distribution?

Back

The range is the difference between the maximum and minimum values in the dataset.