Mathematics, 24.08.2020 22:01 tre9990

The following are the means and standard deviations of some well-known standardized tests, referred to as Test A, Test B, and Test C. All three yield normal distributions. Test Mean Standard deviation
Test A 500 100
Test B 150 8
Test C 70 15

Required:
a. A score of 450 on Test A corresponds to what score on Test B?
b. A score of 625 on Test A corresponds to what score on Test C?

Answers: 3

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Answer from: joeylozier15

(a) A score of 450 on Test A corresponds to a score of 146 on Test B.

(b) A score of 625 on Test A corresponds to a score of 88.75 on Test C.

Step-by-step explanation:

We are given the means and standard deviations of some well-known standardized tests referred to as Test A, Test B, and Test C. All three yield normal distributions.

Test Mean Standard deviation

Test A 500 100

Test B 150 8

Test C 70 15

So, $\mu_A$ = 500 and $\sigma_A$ = 100

$\mu_B$ = 150 and $\sigma_B$ = 8

$\mu_C$ = 70 and $\sigma_C$ = 15

(a) We have to find a score of 450 on Test A corresponds to what score on Test B.

For this, firstly we will find the z-score for a score on Test A and then equate with that of Test B.

z-score of 450 on test A = $\frac{X_A-\mu_A}{\sigma_A}$

= $\frac{450-500}{100}$ = -0.5

So, this z-score corresponds to the score on test B, i.e;

z-score on test B = $\frac{X_B-\mu_B}{\sigma_B}$

-0.5 = $\frac{X_B-150}{8}$

$X_B= 150-(0.5 \times 8)$

= 150 - 4 = 146

Hence, a score of 450 on Test A corresponds to a score of 146 on Test B.

(b) We have to find a score of 625 on Test A corresponds to what score on Test C.

For this, firstly we will find the z-score for a score on Test A and then equate with that of Test C.

z-score of 625 on test A = $\frac{X_A-\mu_A}{\sigma_A}$

= $\frac{625-500}{100}$ = 1.25

So, this z-score corresponds to the score on test C, i.e;

z-score on test C = $\frac{X_C-\mu_C}{\sigma_C}$

1.25 = $\frac{X_C-70}{15}$

$X_C= 70+(1.25 \times 15)$

= 70 + 18.75 = 88.75

Hence, a score of 625 on Test A corresponds to a score of 88.75 on Test C.

Answer from: Quest

the multiples of 15 are 15, 30,45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195, 210, 225, 240, 255, 270, 285, 300, 315, 330, 345, 360, 375, 390, 405, 420, 435, 450, 465, 480, 495, 510, 525, 540, 555, 570, 585, 600, 615, 630, 645, 660, 675, 690, 705, 720, and 735.

the factors of 15 are 1, 3, 5, and 15.

hope that , fam!

-une, your fren : )

Answer from: Quest

2 over 5 and 4 over 15

don’t know last one sorry

step-by-step explanation:

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