Question

lesson assignment #2: section d, e and f. question one 1) on a test, assume $mu = 85$ and $sigma = 7$ a) if a persons raw score is 72, find his z - score. b) if a persons raw score is 88, find his z - score. c) if a persons z - score is 1.9, find their test score. d) if a persons z - score is - 2.2, find their test score.

Explanation:

Step1: Recall 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. We can also re - arrange it to find $x$ as $x = z\sigma+\mu$. Given $\mu = 85$ and $\sigma=7$.

Step2: Solve part a

Substitute $x = 72$, $\mu = 85$, and $\sigma = 7$ into the z - score formula.
$z=\frac{72 - 85}{7}=\frac{- 13}{7}\approx - 1.86$

Step3: Solve part b

Substitute $x = 88$, $\mu = 85$, and $\sigma = 7$ into the z - score formula.
$z=\frac{88 - 85}{7}=\frac{3}{7}\approx0.43$

Step4: Solve part c

Substitute $z = 1.9$, $\mu = 85$, and $\sigma = 7$ into the formula $x = z\sigma+\mu$.
$x=1.9\times7 + 85=13.3+85 = 98.3$

Step5: Solve part d

Substitute $z=-2.2$, $\mu = 85$, and $\sigma = 7$ into the formula $x = z\sigma+\mu$.
$x=-2.2\times7+85=-15.4 + 85=69.6$

Answer:

a) - 1.86
b) 0.43
c) 98.3
d) 69.6