Question

Answer the following:1. Professor Garcia gave a test with a mean score of 73 and a standard deviation of 8.a. What is the z score for someone who scored 73 on the test?b. What is the z score for someone who scored 83 on the test?C.What is the z score for someone who scored 63 on the test?d. Luis had a z score of - 2.5. What was his score on the test?e. Jennifer had a z score of 1.5. What was her score on the test?f. Erin had a z score of 1.77. What was her score on the test?

Answer 1

Solution

- In order to solve the question, we need to know the formula below:

$\begin{gathered} Z=\frac{X-\mu}{\sigma} \\ where, \\ Z=\text{ The Z-score} \\ X=\text{ The individual score} \\ \mu=\text{ The mean score} \\ \sigma=\text{ The standard deviation} \end{gathered}$

- The question has given us the following parameters:

$\begin{gathered} \mu=73 \\ \sigma=8 \end{gathered}$

- With the above information, we can proceed to solve the question as follows:

Question A:

$\begin{gathered} X=73 \\ \therefore Z=\frac{73-73}{8}=\frac{0}{8} \\ \\ Z=0 \end{gathered}$

Question B:

$\begin{gathered} X=83 \\ \therefore Z=\frac{83-73}{8}=\frac{10}{8} \\ \\ Z=\frac{5}{4} \end{gathered}$

Question C:

$\begin{gathered} X=63 \\ Z=\frac{63-73}{8}=-\frac{10}{8} \\ \\ Z=-\frac{5}{4} \end{gathered}$

Question D:

$\begin{gathered} Z=-2.5 \\ \therefore-2.5=\frac{X-73}{8} \\ Cross\text{ multiply,} \\ 8(-2.5)=X-73 \\ Add\text{ 73 to both sides} \\ X=73+8(-2.5) \\ X=53 \end{gathered}$

Question E:

$\begin{gathered} Z=1.5 \\ 1.5=\frac{X-73}{8} \\ Cross\text{ Multiply,} \\ 1.5(8)=X-73 \\ Add\text{ 73 to both sides} \\ X=1.5(8)+73 \\ X=85 \end{gathered}$

Question F:

$\begin{gathered} Z=1.77 \\ 1.77=\frac{X-73}{8} \\ Cross\text{ Multiply,} \\ 8(1.77)=X-73 \\ Add\text{ 73 to both sides} \\ X=73+8(1.77) \\ \therefore X=87.16 \end{gathered}$