Normal curve (100, 4) Normal curve (100, 8) Normal curve (100, 16) 52 68 84 100 116 132 148 52 68 84 100 116 132 148 52 68 84 100 116 132 148 IQ n= 4 n= 16 (a) (b) (c)
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.
7.68 New York City 10-km Run. As reported by Runner’s World magazine, the times of the finishers in the New York City 10-km run are
a. Find the sampling distribution of the sample mean for
b. Repeat part (a) for samples of size 9.
c. Construct graphs similar to those shown in Fig. on page 321.
d. Obtain the percentage of all samples of four finishers that have mean finishing times within 5 minutes of the population mean finishing time of 61 minutes. Interpret your answer in terms of sampling error.
e. Repeat part (d) for samples of size 9.
FIGURE (a) Normal distribution for IQs; (b) sampling distribution of the sample mean for n = 4; (c) sampling distribution of the sample mean for n = 16
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