# The Graduate Record Examination (GRE) is a standardized test that students usually take before entering graduate school. According to the document Interpreting Your GRE Scores, a publication of the Educational Testing Service, the scores on the verbal portion of the GRE are (approximately) normally distributed with mean 462 points and standard deviation 119 points. (6 p.) (a) Obtain and interpret the quartiles for these scores. (b) Find and interpret the 99th percentile for these scores

(a) The first quartile is 382.27 and it means that at least el 25% of the scores are less than 382.27 points.

The second quartile is 462 and it means that at least el 50% of the scores are less than 462 points.

The third quartile is 541.73 and it means that at least el 75% of the scores are less than 541.73 points.

(b) The 99th percentile is 739.27 and it means that at least el 99% of the scores are less than 739.27 points.

Step-by-step explanation:

The first, second the third quartile are the values that let a probability of 0.25, 0.5 and 0.75 on the left tail respectively.

So, to find the first quartile, we need to find the z-score for which:

P(Z<z) = 0.25

using the normal table, z is equal to: -0.67

So, the value x equal to the first quartile is:

Then, the first quartile is 382.27 and it means that at least el 25% of the scores are less than 382.27 points.

At the same way, the z-score for the second quartile is 0, so:

So, the second quartile is 462 and it means that at least el 50% of the scores are less than 462 points.

Finally, the z-score for the third quartile is 0.67, so:

So, the third quartile is 541.73 and it means that at least el 75% of the scores are less than 541.73 points.

Additionally, the z-score for the 99th percentile is the z-score for which:

P(Z<z) = 0.99

z = 2.33

So, the 99th percentile is calculated as:

So, the 99th percentile is 739.27 and it means that at least el 99% of the scores are less than 739.27 points.

## Related Questions

5. The length of similar components produced by a company are approximated by a normal distribution model with a mean of 5 cm and a standard deviation of 0.02 cm. If a component is chosen at random a) what is the probability that the length of this component is between 4.98 and 5.02 cm

the probability that  he length of this component is between 4.98 and 5.02 cm is 0.682 (68.2%)

Step-by-step explanation:

Since the random variable X= length of component chosen at random , is normally distributed, we can define the following standardized normal variable Z:

Z= (X- μ)/σ

where μ= mean of X  , σ= standard deviation of X

for a length between 4.98 cm and 5.02 cm , then

Z₁= (X₁- μ)/σ =  (4.98 cm - 5 cm)/0.02 cm = -1

Z₂= (X₂- μ)/σ = (5.02 cm - 5 cm)/0.02 cm = 1

therefore the probability that the length is between 4.98 cm and 5.02 cm is

P( 4.98 cm ≤X≤5.02 cm)=P( -1 ≤Z≤ 1) = P(Z≤1) - P(Z≤-1)

from standard normal distribution tables we find that

P( 4.98 cm ≤X≤5.02 cm) = P(Z≤1) - P(Z≤-1) = 0.841 - 0.159 = 0.682 (68.2%)

therefore the probability that  he length of this component is between 4.98 and 5.02 cm is 0.682 (68.2%)

The monthly cost (in dollars) of water use is a linear function of the amount of water used (in hundreds of cubic feet, HCF). The cost for using 14 HCF of water is \$ 32.68 , and the cost for using 52 HCF is \$ 95.38 . What is the cost for using 19 HCF of water?

\$40.93

Step-by-step explanation:

### Given

Linear function of:

• 14 HCF = \$32.68
• 52 HCF = \$95.38

To find:

• 19 HCF = ?

### Solution

Linear equation in slope-intercept form:

• y(x) = mx +b

We have points of: (14, 32.68), (52, 95.38):

• y(14) = 14 m + b
• y(52) = 52 m +b

Using the points we can find the value of m and b:

• m= (y2-y1)/(x2-x1)
• m= (95.38 - 32.68)/(52 - 14)
• m = 62.7/ 28
• m= 1.65

Then finding b:

• 14*1.65 +b = 32.68
• b= 32.68 - 23.1
• b= 9.58

So the function is:

• y = 1.65 x + 9.58

Then y(19) is found as:

• y(19) = 1.65*19 + 9.58
• y(19) = 40.93

Answer: Cost of 19 HCF of water is \$40.93

Reynaldo rode his bike 2 miles north and 3 miles east. Which equation should he use to find the distance, d, that takes himdirectly back home?
2²+3² - of
3²-2²-2
of +2² - 3²
2 + 3²= 2²

I would say it would be D

Step-by-step explanation:

Step-by-step explanation:

A ball is thrown downward from the top of a building with an initial speed of 25 m/s. It strikes the ground after 2.0 s. How high is the building, assuming negligible air resistance

Use one of the equations of motion under constant acceleration:-

s = ut + 0.5at^2   where s = distance, u - initial velocity, a = acceleration ( in this case it is gravity = 9.81 m s^-2)  and t = time.

here we have s = 25*2 + 0.5*9.81 * 2^2

Answer: The height of the building is 69.6 m

Explanation:

To calculate the height of the building, we use second equation of motion:

where,

s = height of the building = ?

u = initial velocity of the ball = 25 m/s

a = acceleration due to gravity =

t = time taken = 2.0 sec

Putting values in above equation, we get:

Hence, the height of the building is 69.6 m

−1.75 − 22/20
plz hlep
...and put as an exact decimal or simplified fraction

-2.85

Step-by-step explanation:

I looked it up tbh

-2.85

Step-by-step explanation:

Google it or Edge it or Firefox it

let d equal the distance in meters and t equal the time in seconds. Which is a direct variation equation for this relationship