Question

1. scores on the teacher training college entrance exam had a mean of 50 and standard deviation of 5. martins standard score on the examination was ( z = 2.0 ). what was martins actual examination score?

a. 40
b. 50
c. 52
d. 60

Explanation:

Step1: Recall the z - score formula

The z - score formula is \(z=\frac{x-\mu}{\sigma}\), where \(x\) is the raw score, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.

Step2: Substitute the given values into the formula

We are given that \(z = 2.0\), \(\mu=50\), and \(\sigma = 5\). Substituting these into the formula \(2.0=\frac{x - 50}{5}\).

Step3: Solve for \(x\)

Multiply both sides of the equation by \(5\): \(2.0\times5=x - 50\). So, \(10=x - 50\). Then add \(50\) to both sides: \(x=10 + 50\).

Answer:

\(x = 60\), so the answer is D.