Question

Please Help will medal!!! :D

1. The scores for all high school seniors taking the verbal section of the Scholastic Aptitude Test (SAT) is a normal distribution and in a particular year had a mean of 490 and a standard deviation of 100.

a.If a student had a z-score of 1.8, how much higher would he have scored on the test than someone who had a z-score of -.3?

Answer 1

`.If a student had a z-score of 1.8` then what is the raw score x?

Use this formula to determine the answer

\[\Large z = \frac{x - \mu}{\sigma}\]
In this case,
\[\Large \mu = \text{mean} = 490\]
\[\Large \sigma = \text{standard deviation} = 100\]

Answer 2

\[\Large z = \frac{x - \mu}{\sigma}\]
\[\Large 1.8 = \frac{x - 490}{100}\]
solve for x

Answer 3

Would the raw score be -4.9? :)

Answer 4

no, it should be close to 490

Answer 5

the positive z score means the raw score (x) is above 490

Answer 6

Step 1) z score formula
Step 2) plug in the given values
Step 3) Multiply both sides by 100
Step 4) Multiply and simplify (notice the cancelation on the right side)
Step 5) Add 490 to both sides
Step 6) Combine like terms


\[\Large {\color{green}{\text{Step 1)}}} \ \ z = \frac{x - \mu}{\sigma}\]
\[\Large {\color{green}{\text{Step 2)}}} \ \ 1.8 = \frac{x - 490}{100}\]
\[\Large {\color{green}{\text{Step 3)}}} \ \ 100*1.8 = 100*\frac{x - 490}{100}\]
\[\Large {\color{green}{\text{Step 4)}}} \ \ 180 = x-490\]
\[\Large {\color{green}{\text{Step 5)}}} \ \ 180+490 = x-490+490\]
\[\Large {\color{green}{\text{Step 6)}}} \ \ 670 = x\]

So the z score of z = 1.8 corresponds to the raw score of x = 670

Answer 7

ohh ok i was looking for the raw score of z

Answer 8

If the z-score is -0.3, then what is the raw score x?

Answer 9

z = -0.3 means x = ???

Answer 10

460 right?

Answer 11

yes

Answer 12

z = -0.3 leads to x = 460

notice how this raw score is below the mean (490)

Answer 13

yes

Answer 14

so you'll now subtract the raw scores
x = 670 and x = 460

Answer 15

210? :)

Answer 16

correct

Answer 17

210 is your final answer

Answer 18

ah ok thankyou! is it ok if i ask for help on another question :)

Answer 19

sure go ahead

Answer 20

2. Bob takes a test in English and gets an 85%. The mean of the English class is 76% with a standard deviation of 5%. Sally takes a math test and she gets an 85%. The mean in math class is 62% with a standard deviation of 12%. Who did relatively better on their test compared to their classmates? Explain your answer using z-scores.

Answer 21

You'll use this formula again
\[\Large z = \frac{x - \mu}{\sigma}\]

Answer 22

The english class has
mu = 0.76
sigma = 0.05

what is the z score if the raw score is x = 0.85 ?

Answer 23

1.8? :)

Answer 24

correct

Answer 25

The math class has
mu = 0.62
sigma = 0.12

if x = 0.85 then z = ???

Answer 26

1.92 right ?

Answer 27

yes after you round

Answer 28

so because Sally has the higher z-score, she did better relative to her classmates

Answer 29

Thankyou so much!!

Answer 30

no problem