To determine the math SAT score that is 1.5 standard deviations above the mean, let's proceed step by step:
1. Identify the Mean (μ) and Standard Deviation (σ):
- The mean (μ) of the math SAT scores is 520.
- The standard deviation (σ) of the math SAT scores is 115.
2. Calculate the score that is 1.5 standard deviations above the mean:
- To find the score that is 1.5 standard deviations above the mean, we can use the following formula:
[tex]\[
\text{Score} = \mu + (k \times \sigma)
\][/tex]
where [tex]\( k \)[/tex] is the number of standard deviations above the mean.
- In this case, [tex]\( k = 1.5 \)[/tex]. So,
[tex]\[
\text{Score} = 520 + (1.5 \times 115)
\][/tex]
3. Evaluate the expression:
- First, multiply the standard deviation by 1.5:
[tex]\[
1.5 \times 115 = 172.5
\][/tex]
- Then, add this value to the mean:
[tex]\[
520 + 172.5 = 692.5
\][/tex]
4. Round the result to a whole number:
- To present the score as a whole number, we round 692.5 to the nearest integer.
[tex]\[
692.5 \approx 692
\][/tex]
Therefore, the math SAT score that is 1.5 standard deviations above the mean is 692 when rounded to the nearest whole number.
