Understanding Probability in Normal Distribution

This video tutorial explains how to use tables to find probabilities in a normal distribution. It covers calculating the probability of a data value being below, above, or between given values using z-scores. Two examples are provided: one for values below and above 85, and another for values between 75 and 110. The tutorial demonstrates using z-score tables and symmetry for negative z-scores, highlighting potential rounding errors.

What is the purpose of using tables in normal distribution probability calculations?

• To find the mean and standard deviation

• To determine the probability of data values

• To calculate the median of the data set

• To identify outliers in the data

In the first example, what is the mean of the data set?

• 0.75

• 85

• 20

• 100

How is the z-score calculated?

• Standard deviation divided by data value minus mean

• Mean minus data value divided by standard deviation

• Data value plus mean divided by standard deviation

• Data value minus mean divided by standard deviation

What is the z-score for a data value of 85 in the first example?

• -1.25

• 1.25

• -0.75

• 0.75

What type of z-score table gives the area from 0 to a given z-score?

• Cumulative table

• Negative z-score table

• Symmetrical table

• 0 through z table

What is the probability that x is less than 85 in the first example?

• 0.2734

• 0.2266

• 0.5

• 0.7734

In the second example, what is the z-score for a data value of 75?

• -1.25

• 0.5

• -0.5

• 1.25

What is the combined probability of a data value being between 75 and 110?

• 0.5859

• 0.1915

• 0.7734

• 0.3944

Why might there be a slight rounding error in the probability calculations?

• Because of rounding to the fourth decimal place

• Because of using negative z-scores

• Due to incorrect z-scores

• Due to incorrect table values

What is the standard deviation of the data set in both examples?

• 100

• 0.75

• 20

• 85