To find the data point \( x \) that would result in a z-score of 1.6, we can use the formula for the z-score:
\[ z = \frac{x - \mu}{\sigma} \]
where:
- \( z \) = z-score
- \( \mu \) = population mean
- \( \sigma \) = standard deviation
- \( x \) = data point
We know the following values:
- \( z = 1.6 \)
- \( \mu = 135 \)
- \( \sigma = 5 \)
Now, we can substitute these values into the formula and solve for \( x \):
\[ 1.6 = \frac{x - 135}{5} \]
Now, multiply both sides by 5:
\[ 1.6 \times 5 = x - 135 \]
\[ 8 = x - 135 \]
Next, add 135 to both sides:
\[ x = 8 + 135 \]
\[ x = 143 \]
Thus, the data point \( x \) that would result in a z-score of 1.6 is
\[ \boxed{143} \]