Instructions: Use the empirical rule to find the following probabilities. Remember to draw a normal curve, label the x-values for 1, 2, and 3 standard deviations from the mean, and write in the probabilities between each standard deviation before answering the questions. Suppose that the scores on a national achievement exam have a mean of 480 and a standard deviation of 90. What score is 3 standard deviations above the mean? What score is 2 standard deviations below the mean? Approximately 68% will fall between and Approximately 99.7% will fall between and What is the probability that a randomly selected student will score at least a 300? % What is the probability that a student will score at most a 390? %
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
