Empirical Rule Homwwork

Front

What is the Empirical Rule?

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 one standard deviation of the mean in a normal distribution?

Back

68%.

Front

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

Back

95%.

Front

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

Back

99.7%.

Front

What shape is a normal distribution curve?

Back

Bell curve.

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 all tires?

Back

28,000 km and 32,000 km.

Front

In a normal distribution, what percentage of data is found in the tails beyond two standard deviations?

Back

5%.

Front

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

Back

The standard deviation measures the dispersion or spread of the data points around the mean.

Front

If a normal distribution has a mean of 50 and a standard deviation of 10, what is the range for 95% of the data?

Back

30 to 70.

Front

What does it mean if data is normally distributed?

Back

It means that the data follows a symmetric bell-shaped curve where most of the observations cluster around the central peak.