Question

given a population mean of 135 and a standard deviation of 5, what data point, x, would result in a z - score of 1.87 (1 point)
140
143
152
137

Explanation:

Step1: Recall the z - score formula

The z - score formula is \(z=\frac{x - \mu}{\sigma}\), where \(z\) is the z - score, \(x\) is the data point, \(\mu\) is the population mean, and \(\sigma\) is the population standard deviation.
We are given that \(\mu = 135\), \(\sigma=5\), and \(z = 1.67\).

Step2: Solve the formula for \(x\)

Starting with \(z=\frac{x-\mu}{\sigma}\), we can multiply both sides by \(\sigma\) to get \(z\sigma=x - \mu\).
Then add \(\mu\) to both sides: \(x=\mu+z\sigma\).

Step3: Substitute the given values

Substitute \(\mu = 135\), \(z = 1.67\), and \(\sigma = 5\) into the formula \(x=\mu+z\sigma\).
\(x=135+(1.67\times5)\)
First, calculate \(1.67\times5 = 8.35\).
Then \(x=135 + 8.35=143.35\approx143\)

Answer:

143