Question

On a measure of artistic abilities the mean for college students in New Zealand is 150 and a standard deviation is 25 give the Z scores for New Zealand college students who score A100 B120 C140 and D160 give the raw scores for persons whose the Z scores on the test are E -1 F -8 G -2 and H 1.38

Answer 1

The method for computing a z-score is  $\bold{z = \frac{(x-\mu)}{\sigma}}$, where x is the crude score, $\bold{\mu}$ is the mean population, and $\bold{\sigma}$ seems to be the standard population difference.

• The Z value of x is a number $\bold{\frac{(x - \text{mean(series))}}{\text{SD(series)}}}$ are defined where SD is the standard deviation.
• Here, we consider series as scores of students of colleges in New Zealand for their artistic abilities.

$\bold{\bar{x}=150}\\\\ \bold{\sigma=25}$

following are the calculation of the Z scores:

$\to \ (a)\ 100:\ \text{Z score}=\frac{(100-150)}{25}= \frac{(-50)}{25} = -2\\\\\to \ (b)\ 120:\ \text{Z score}=\frac{(120-150)}{25}= \frac{(-30)}{25} = -1.2\\\\\to \ (c)\ 140:\ \text{Z score}=\frac{(140-150)}{25}= \frac{(-10)}{25} = -0.4\\\\\to \ (a)\ 160:\ \text{Z score}=\frac{(160-150)}{25}= \frac{(10)}{25} = 0.4$

Using formula:

$\to \text{Raw score = Mean(series) +Z score} \times \text{SD(series)}$

Calculating the Raw scores:

$\text{(e) -1: Raw score= 150 +(-1)} \times 25 = 125 \\\\\text{(f) -0.8: Raw score= 150 +(-0.8)} \times 25 = 130\\\\\text{(e) -0.2: Raw score= 150 +(-0.2)} \times 25 = 145\\\\\text{(e) 1.38: Raw score= 150 +(1.38)} \times 25 = 184.5$

Learn more:

brainly.com/question/12865701