Normal Distribution -empirical rule

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 one standard deviation of the mean, about 95% falls within two standard deviations, and about 99.7% falls within three standard deviations.

Front

How much of the data falls within 1 standard deviation according to the Empirical Rule?

Back

Approximately 68%.

Front

How much of the data falls within 2 standard deviations according to the Empirical Rule?

Back

Approximately 95%.

Front

How much of the data falls within 3 standard deviations according to the Empirical Rule?

Back

Approximately 99.7%.

Front

If a normal distribution has a mean of 75 and a standard deviation of 7, what is the z-score for a value of 68?

Back

The z-score is -1 (calculated as (68-75)/7).

Front

In a normal distribution, what does a z-score represent?

Back

A z-score represents the number of standard deviations a data point is from the mean.

Front

Given a mean of 75 and a standard deviation of 7, how many students out of 500 would score higher than 68?

Back

Approximately 420 students.

Front

If the ages of golfers are normally distributed with a mean of 38 and a standard deviation of 4, how many members are younger than 34?

Back

Approximately 80 members.

Front

What does it mean if a data point is one or more standard deviations above the mean in a normal distribution?

Back

It indicates that the data point is significantly higher than the average, representing a higher percentile in the distribution.

Front

Given a mean of 75 and a standard deviation of 7, how many students out of 500 would score between 68 and 82?

Back

Approximately 340 students.