Answer :
Final answer:
The probability that someone scores between 300 and 650 on the SAT, given that the mean is 500 and the standard deviation is 100, and assuming a normal distribution, is approximately 90.8%.
Explanation:
This question is related to the field of Statistics, particularly the concept of Standard Deviation and z-score in a Normal Distribution. The z-score is a measure of how many standard deviations an element is from the mean. In this case, if the mean of the SAT score is 500 and the standard deviation is 100, we can calculate the z-scores for 300 and 650 by subtracting the mean and dividing by the standard deviation like so:
Z1 = (300 - 500) / 100 = -2
Z2 = (650 - 500) / 100 = 1.5
Therefore, we want the probability that the Z is between -2 and 1.5 in a standard normal distribution. Using a standard z-table or calculator, we find P(-2 < Z < 1.5) would roughly equal to 0.908, or 90.8%. So, there is approximately a 90.8% chance someone will score between 300 and 650 on the SAT assuming the scores follow a normal distribution.
Learn more about Standard Deviation here:
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