The College Board reported the following mean scores for the three parts of the Scholastic Aptitude Test (SAT) (The World Almanac, 2009): Critical Reading 502 Writing 494 Assume that the population standard deviation on each part of the test is = 100. Use z-table. What is the probability a sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 502 on the Critical Reading part of the test (to 4 decimals)? Round z value in intermediate calculation to 2 decimals places. What is the probability a sample of 100 test takers will provide a sample mean test score within 10 points of the population mean of 494 on the writing part of the test (to 4 decimals)? Round z value in intermediate calculation to 2 decimals places.
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.
The College Board reported the following
| Critical Reading | 502 |
| Writing | 494 |
Assume that the population standard deviation on each part of the test is = 100. Use z-table.
- What is the
probability a sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 502 on the Critical Reading part of the test (to 4 decimals)?
Round z value in intermediate calculation to 2 decimals places. - What is the probability a sample of 100 test takers will provide a sample mean test score within 10 points of the population mean of 494 on the writing part of the test (to 4 decimals)?
Round z value in intermediate calculation to 2 decimals places.
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