Answer :
To calculate the z-score for a data point, we use the formula:
[tex]\[ z = \frac{x - \text{mean}}{\text{standard deviation}} \][/tex]
Let's break this down with the given data:
1. Identify the values:
- The sample mean ([tex]\(\text{mean}\)[/tex]) is 34.4.
- The sample standard deviation ([tex]\(\text{standard deviation}\)[/tex]) is 3.7.
- The data point ([tex]\(x\)[/tex]) we're interested in is 35.8.
2. Plug the values into the z-score formula:
[tex]\[ z = \frac{35.8 - 34.4}{3.7} \][/tex]
3. Calculate the difference in the numerator:
[tex]\[ 35.8 - 34.4 = 1.4 \][/tex]
4. Divide the difference by the standard deviation:
[tex]\[ z = \frac{1.4}{3.7} \approx 0.378 \][/tex]
5. Round the result to two decimal places:
The z-score is approximately 0.38.
Therefore, the z-score for the data point [tex]\(x = 35.8\)[/tex] is 0.38.
[tex]\[ z = \frac{x - \text{mean}}{\text{standard deviation}} \][/tex]
Let's break this down with the given data:
1. Identify the values:
- The sample mean ([tex]\(\text{mean}\)[/tex]) is 34.4.
- The sample standard deviation ([tex]\(\text{standard deviation}\)[/tex]) is 3.7.
- The data point ([tex]\(x\)[/tex]) we're interested in is 35.8.
2. Plug the values into the z-score formula:
[tex]\[ z = \frac{35.8 - 34.4}{3.7} \][/tex]
3. Calculate the difference in the numerator:
[tex]\[ 35.8 - 34.4 = 1.4 \][/tex]
4. Divide the difference by the standard deviation:
[tex]\[ z = \frac{1.4}{3.7} \approx 0.378 \][/tex]
5. Round the result to two decimal places:
The z-score is approximately 0.38.
Therefore, the z-score for the data point [tex]\(x = 35.8\)[/tex] is 0.38.
