The scores on the Accuplacer test and High School GPAs are normally distributed. The Accuplacer test had a mean of 30 and a standard deviation of 10. High School GPAs had a mean of 2.5 and a standard deviation of 0.1. What high school GPA do you need to equal a score of 22 on the Accuplacer test? Give answer to two decimal places.

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The scores on the Accuplacer test and High School GPAs are normally distributed.
The Accuplacer test had a mean of 30 and a standard deviation of 10.
High School GPAs had a mean of 2.5 and a standard deviation of 0.1.
What high school GPA do you need to equal a score of 22 on the Accuplacer test?
Give answer to two decimal places.

 

For data that is not normally distributed we can't use z-scores. However, there is an equation that works on any distribution. It's called Chebyshev's formula. The formula is  where P=1- 1/k2 p is the minimum percentage of scores that fall within kk standard deviations on both sides of the mean. Use this formula to answer the following questions.

a) If you have scores and you don't know if they are normally distributed, find the minimum percentage of scores that fall within 3.3 standard deviations on both sides of the mean?   

b) If you have scores that are normally distributed, find the percentage of scores that fall within 3.3 standard deviations on both sides of the mean?   

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