Answer :
To find the [tex]\(x\)[/tex]-value that corresponds to the [tex]\(z\)[/tex]-score of 2.575, we use the formula:
[tex]\[ x = \mu + z\sigma \][/tex]
Where:
- [tex]\( \mu \)[/tex] is the mean of the scores
- [tex]\( z \)[/tex] is the [tex]\( z \)[/tex]-score
- [tex]\( \sigma \)[/tex] is the standard deviation
Given:
- The mean ([tex]\(\mu\)[/tex]) is 77
- The standard deviation ([tex]\(\sigma\)[/tex]) is 8
- The [tex]\( z \)[/tex]-score is 2.575
Substitute these values into the formula:
[tex]\[ x = 77 + (2.575 \times 8) \][/tex]
First, calculate the product of the [tex]\( z \)[/tex]-score and the standard deviation:
[tex]\[ 2.575 \times 8 = 20.6 \][/tex]
Now, add this result to the mean:
[tex]\[ x = 77 + 20.6 = 97.6 \][/tex]
Therefore, the [tex]\(x\)[/tex]-value that corresponds to the [tex]\(z\)[/tex]-score 2.575 is 97.6. So, the correct answer is:
d. 97.6
[tex]\[ x = \mu + z\sigma \][/tex]
Where:
- [tex]\( \mu \)[/tex] is the mean of the scores
- [tex]\( z \)[/tex] is the [tex]\( z \)[/tex]-score
- [tex]\( \sigma \)[/tex] is the standard deviation
Given:
- The mean ([tex]\(\mu\)[/tex]) is 77
- The standard deviation ([tex]\(\sigma\)[/tex]) is 8
- The [tex]\( z \)[/tex]-score is 2.575
Substitute these values into the formula:
[tex]\[ x = 77 + (2.575 \times 8) \][/tex]
First, calculate the product of the [tex]\( z \)[/tex]-score and the standard deviation:
[tex]\[ 2.575 \times 8 = 20.6 \][/tex]
Now, add this result to the mean:
[tex]\[ x = 77 + 20.6 = 97.6 \][/tex]
Therefore, the [tex]\(x\)[/tex]-value that corresponds to the [tex]\(z\)[/tex]-score 2.575 is 97.6. So, the correct answer is:
d. 97.6