Answer :
Answer: The student's SAT score of 795 is significantly higher than the mean score of 490 for all high school seniors. To better understand how this student's score compares to the rest of the students' scores, we can utilize the concept of standard deviations.
Given:
- Mean score () = 490
- Standard deviation () = 100
- Student's score = 795
To determine how many standard deviations above the mean the student's score is, we can use the formula for z-score:
where:
- is the student's score (795)
- is the mean score (490)
- is the standard deviation (100)
Substitute the values into the formula:
This means that the student's score of 795 is 3.05 standard deviations above the mean. In a normal distribution (bell-shaped curve), a score that is more than 2 standard deviations away from the mean is considered significantly higher than the majority of scores.
Therefore, the student's score of 795 is well above the majority of high school seniors who took the verbal section SAT that year.
Step-by-step explanation:
The person with an ACT score of 30 did better as the Z-score is higher.
Z-score Calculation:
Z-score for 720: Z = (720 - 520) / 115 = 1.74. This means a score of 720 is 1.74 standard deviations above the mean.
Math Score 1.5 SD above mean: 520 + 1.5(115) = 692.5. The score 692.5 is 1.5 standard deviations above the mean of 520.
Comparing SAT and ACT scores: Z-score for SAT score of 700: (700 - 514) / 117 = 1.59. Z-score for ACT score of 30: (30 - 21) / 5.3 = 1.70. The person with an ACT score of 30 did better as the Z-score is higher.
