Statistics

What is the total area under the normal​ curve?

1

As the size of a sample​ increases, the mean of the distribution of sample means increases.

False. As the size of a sample​ increases, the mean of the distribution of sample means does not change.

Standard Normal Distribution Statements (8)

It is unimodal (continuous) it is symmetric about 0 its standard deviation is 1 It is bell shaped mean=median=mode curve never touches axis total area under curve = 1 empirical rule

z-score

Measure of position that gives the number of standard deviations hat a data value x falls above or below the mean of its data set

In a normal​ distribution, which is​ greater, the mean or the​ median? Explain.

Neither; in a normal​ distribution, the mean and median are equal.

If a​ z-score is​ zero, which of the following must be​ true? Explain your reasoning. • The mean is zero. • The corresponding​ x-value is zero. • The corresponding​ x-value is equal to the mean.

The corresponding​ x-value is equal to the​ mean, because the​ z-score is equal to the difference between the​ x-value and the​ mean, divided by the standard deviation.

It is impossible to have a​ z-score of 0.

The statement is false. A​ z-score of 0 is a standardized value that is equal to the mean.

A​ student's score on an actuarial exam is in the 78th percentile. What can you conclude about the​ student's exam​ score?

The student scored higher than​ 78% of the students who took the actuarial exam.