Understanding Normal Distribution

The video tutorial explains the properties of a normal distribution, highlighting that the mean, median, and mode are equal and located at the center. It introduces the concept of standard deviation and uses the empirical rule to describe how data is distributed around the mean. The tutorial provides a step-by-step calculation of the standard deviation using the intervals defined by the empirical rule, demonstrating that the standard deviation is 12 for the given data set.

What is a key property of the normal distribution regarding its mean, median, and mode?

• They are all negative.

• They are all equal.

• They are all zero.

• They are all different.

In a normal distribution, where are the mean, median, and mode located?

• At the right tail of the distribution

• At the left tail of the distribution

• At the top of the distribution

• At the center of the distribution

According to the empirical rule, approximately what percentage of data falls within one standard deviation of the mean?

• 68%

• 50%

• 99.7%

• 95%

What is the range of data that falls within two standard deviations from the mean in a normal distribution?

• 36 to 108

• 72 to 84

• 60 to 84

• 48 to 96

What percentage of data falls within three standard deviations from the mean according to the empirical rule?

• 68%

• 95%

• 99.7%

• 100%

If the mean of a normal distribution is 72, what is the value of one standard deviation if the range is from 60 to 84?

• 6

• 12

• 36

• 24

How do you calculate the standard deviation if the numbers are not straightforward?

• By setting up an equation

• By using the empirical rule

• By guessing

• By measuring the graph

What equation would you set up to find the standard deviation if the mean is 72 and the upper bound is 84?

• 72 + sigma = 84

• 72 * sigma = 84

• 72 - sigma = 84

• 72 / sigma = 84

What is the result of subtracting the mean from the upper bound in the equation to find the standard deviation?

• 0

• 6

• 12

• 24

What is the standard deviation if the mean is 72 and the range is from 60 to 84?

• 6

• 24

• 12

• 18