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?(1 point)
x=

Answer 1

To find the data point \( x \) that corresponds to a z-score of 1.6, you can use the formula for the z-score:

\[
z = \frac{x - \mu}{\sigma}
\]

where:
- \( z \) is the z-score,
- \( \mu \) is the population mean, and
- \( \sigma \) is the standard deviation.

Given:
- \( z = 1.6 \)
- \( \mu = 135 \)
- \( \sigma = 5 \)

You can rearrange the formula to solve for \( x \):

\[
x = z \sigma + \mu
\]

Substituting the given values into the equation:

\[
x = (1.6)(5) + 135
\]

Calculating this step-by-step:

1. Calculate \( (1.6)(5) = 8 \)
2. Add \( 135 + 8 = 143 \)

So, the data point \( x \) that results in a z-score of 1.6 is:

\[
x = 143
\]