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.