z-Scores and Area under the Curve A researcher collected data on adults using an intelligence test. The data for these adults were approximately normally distributed with the following mean and standard deviation mean = 102 points standard deviation = 13 points Use this information and the online normal distribution calculator to answer the questions below. Round your percents to two decimal places. Note: Use z-scores rounded to 2 decimal places and the standard normal distribution to avoid roundoff errors. Normal Calculator If an adult is randomly selected from the study, what is the probability the adult scored between 113 points and 125 points? ______% If an adult is randomly selected from the study, what is the probability the adult scored less than 110.7 points? % If an adult is randomly selected from the study, what is the probability the adult scored more than 127.7 points? _______% If an adult is randomly selected from the study, what is the probability the adult scored less than 67.4 points or more than 131.7 points? _____%
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.
z-Scores and Area under the Curve
A researcher collected data on adults using an intelligence test. The data for these adults were approximately
mean =
102
points
standard deviation =
13
points
Use this information and the online normal distribution calculator to answer the questions below. Round your percents to two decimal places.
Note: Use z-scores rounded to 2 decimal places and the standard normal distribution to avoid roundoff errors.
Normal Calculator
If an adult is randomly selected from the study, what is the
113
points and
125
points?
______%
If an adult is randomly selected from the study, what is the probability the adult scored less than
110.7
points?
%
If an adult is randomly selected from the study, what is the probability the adult scored more than
127.7
points?
_______%
If an adult is randomly selected from the study, what is the probability the adult scored less than
67.4
points or more than
131.7
points?
_____%
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