Scores on the GRE. A college senior who took the Graduate Record Examination exam scored 560 on the Verbal Reasoning section and 740 on the Quantitative Reasoning section. The mean score for Verbal Reasoning section was 460 with a standard deviation of 132, and the mean score for the Quantitative Reasoning was 452 with a standard deviation of 140. Suppose that both distributions are nearly normal. Round calculated answers to 4 decimal places unless directed otherwise.
(a) Write down the short-hand for these two normal distributions
(b) What is her Z score on the Verbal Reasoning section? On the Quantitative Reasoning section? Draw a standard normal distribution curve and mark these two Z scores.
(c) What do these Z scores tell you?
(d) Relative to others, which section did she do better on?
(e) Find her percentile scores for the two exams.
(f) What percent of the test takers did better than her on the Verbal Reasoning section? On the Quantitative Reasoning section?

Kindly check explanation

Step-by-step explanation:

Verbal:

Score, x = 560

Mean, m = 460

Standard deviation, s = 132

Quantitative :

Score, x = 740

Mean, m = 452

Standard deviation, s = 140

a)

Verbal :

X ~ N(460, 132)

Quantitative :

X ~ N(452, 140)

(b)

What is her Z score on the Verbal Reasoning section? On the Quantitative Reasoning section? Draw a standard normal distribution curve and mark these two Z scores.

Zscore = (x - m) / s

Verbal :

Zscore = (560 - 460) / 132 = 0.758

Quantitative :

Zscore = (740 - 452) /140 = 2.057

(c.)

He has a higher standardized score in the quantitative than the verbal score.

(d.)

The Zscore shows that he performed better in the quantitative reasoning than verbal.

(e) Find her percentile scores for the two exams.

(f) What percent of the test takers did better than her on the Verbal Reasoning section? On the Quantitative Reasoning section?

Verbal :

Score greater than 560

P(x > 560) :

Z = (560 - 460) / 132 = 0.758

P(Z > 0.758) = 0.22423 = 22.4%

Quantitative :

Score greater than 740

P(x > 740) :

Z = (740 - 452) / 140 = 2.057

P(Z > 0.758) = 0.0198 = 1.98%

mr. flanders’ class sold 47 doughnuts and   mr. rodriquez’s class sold 38 cartons of milk

step-by-step explanation:

let x be the number of doughnuts sold by mr. flanders’ class and y be the number of cartons sold by mr. rodriquez’s class.

1. together, the classes sold 85 items, then

x+y=85.

2. both classes earn earned $104.49 for their school. if doughnuts were sold for $1.35 each, then x doughnuts costed $1.35x. if cartons of milk were sold for $1.08 each, then y cartons costed $1.08y. hence,

1.35x+1.08y=104.49.

3. solve the system of two equations:

hm let me think hm think think hm think yes