SOLVE THE GIVEN PROBLEMS. SHOW THE STEP-BY-STEP SOLUTION. 1. Ruben's score in the National Achievement Test (NAT) in Math was 38. He wants to find out his relative standing on the said test so he researched the average performance of the NAT-takers. He found out that the population mean score was 25 and the standard deviation was 3. What was Ruben's score in z-score? What is the conclusion? 2. Javin has a towing business. His son Michael would like to know the status of his father's business so he researched the ratings of towing businesses in the city. Given the mean, x̄ = 3, and the standard deviation, s = 0.5, help Michael find the z-value that corresponds to Javin's rating score of X = 4.5. What is the conclusion?
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.
SOLVE THE GIVEN PROBLEMS. SHOW THE STEP-BY-STEP SOLUTION.
1. Ruben's score in the National Achievement Test (NAT) in Math was 38. He wants to find out his relative standing on the said test so he researched the average performance of the NAT-takers. He found out that the population mean score was 25 and the standard deviation was 3. What was Ruben's score in z-score?
What is the conclusion?
2. Javin has a towing business. His son Michael would like to know the status of his father's business so he researched the ratings of towing businesses in the city. Given the mean, x̄ = 3, and the standard deviation, s = 0.5, help Michael find the z-value that corresponds to Javin's rating score of X = 4.5.
What is the conclusion?
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