For the majority of maths tests taken at a school, it is shown that the test score is approximaly normally distributed with a mean of 100 and a standard deviation of 15. i. If the random variable ?, is the math test score, state the value/s of its parameter/s. ii. Find the probability that a random score lies between 90 and 115. iii. Find the probability that the average of nine random scores lies between 90 and 115.
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.
For the majority of maths tests taken at a school, it is shown that the test score is approximaly
i. If the random variable ?, is the math test score, state the value/s of its parameter/s.
ii. Find the probability that a random score lies between 90 and 115.
iii. Find the probability that the average of nine random scores lies between 90 and 115.
iv. Find the test score ? for which 67% of scores are less than ?.
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