Question

Given a population mean of 135 and a standard deviation of 5, what data point, x, would result in a z-score of 1.6? (Hint: use formula x−μσ=z−score
)(1 point)
x=

Answer 1

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

\[
\boxed{143}
\]