Every year thousands of students take the SAT'S. RECENT TRENDS SHOW THAT THE SCORES ON THE VERBAL SECTION FOLLOW AN APPROX. NORMAL DISTRIBUTION WITH MEAN 550 AND STANDARD DEVIATION OF 110
68.26% OF THE STUDENTS WHO TAKE THE SAT VERBAL SCORE BETWEEN ______ AND _____
95.44% OF STUDENTS WHO TAKE THE SAT VERBAL SCORE BETWEEN ____ AND ____
99.74 % OF THE STUDENTS WHO TAKE THE SAT VERBAL SCORE BETWEEN ____AND ____
You have the mean 550 which is in the center of the normal distribution curve. and standard deviation is 110 which is how far the score is away from the mean.
The question is asking you for 68.26, 95.44 and 99.74 percents and is demonstrated by the emperical rule that 68.26% is one standard deviation away from the mean, 95.44% is 2 standard deviations away from the mean and 99.74% is 3 standard deviations away from the mean.
so, 68.26% wud just be 550+or- 110, or between 440 and 660
95.44% is 2 standard deviations away from the mean so it wud be 550+or-2(110) or between 330 and 770
finally the 99.74% is 3 standard deviations away from the mean so it wud be 550+or-3(110) or between 220 and 880 (which doesn't make sense cuz no one can get 880 on a verbal sat score) :D
To fill in the missing values, we need to use the properties of the normal distribution and z-scores. A z-score measures how many standard deviations a particular value is from the mean. We can use z-scores to find the percentage of students who score between certain values.
To find the range of scores for the first two percentages, we need to determine the z-scores that correspond to those percentages.
68.26% falls within one standard deviation of the mean, so we calculate it as follows:
- Subtracting one standard deviation from the mean: 550 - 110 = 440
- Adding one standard deviation to the mean: 550 + 110 = 660
Therefore, 68.26% of students who take the SAT verbal score between 440 and 660.
Similarly, to find the range of scores for 95.44%, we calculate the z-scores for the two ends of the percentage range:
- Subtracting two standard deviations from the mean: 550 - (2 * 110) = 330
- Adding two standard deviations to the mean: 550 + (2 * 110) = 770
Therefore, 95.44% of students who take the SAT verbal score between 330 and 770.
Lastly, to find the range of scores for 99.74%, we calculate the z-scores for the two ends of the percentage range:
- Subtracting three standard deviations from the mean: 550 - (3 * 110) = 220
- Adding three standard deviations to the mean: 550 + (3 * 110) = 880
Therefore, 99.74% of students who take the SAT verbal score between 220 and 880.
In summary:
- 68.26% of students who take the SAT verbal score between 440 and 660.
- 95.44% of students who take the SAT verbal score between 330 and 770.
- 99.74% of students who take the SAT verbal score between 220 and 880.