MATHEMATICS HIGH SCHOOL

Eleanor scores 680 on the mathematics part of the SAT. The distribution of SAT math scores in recent years has been Normal with mean 513 and standard deviation 81. Gerald takes the ACT Assessment mathematics test and scores 27. ACT math scores are Normally distributed with mean 22.7 and standard deviation 4.What is Elanor's standardized score?

Answers

Answer 1

Answer:

Answer:

$z =(680-513)/(81)=2.06$

The Eleanor score is 2.06 deviations above the mean.

$z =(27-22.7)/(4)=1.08$

The Gerald score is 1.08 deviations above the mean.

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Part a

Let X the random variable that represent the SAT scores of a population, and for this case we know the distribution for X is given by:

$X \sim N(513,81)$

Where $\mu=513$ and $\sigma=81$

For this case we can calculate the z score with the following formula:

$z=(X-\mu)/(\sigma)$

And if we replace we got:

$z =(680-513)/(81)=2.06$

So the Eleanor score is 2.06 deviations above the mean.

Part b

Let X the random variable that represent the ACT scores of a population, and for this case we know the distribution for X is given by:

$X \sim N(22.7,4)$

Where $\mu=22.7$ and $\sigma=4$

For this case we can calculate the z score with the following formula:

$z=(X-\mu)/(\sigma)$

And if we replace we got:

$z =(27-22.7)/(4)=1.08$

So the Gerald score is 1.08 deviations above the mean.

Related Questions

78 is 15%, percent of what number?
The sum of a number m and 7.1
The demand and supply functions for bikes are p=900−⁰.¹ and p=3⁰.⁹ respectively. Where p is the price, and the quantity. What is the consumer surplus at equilibrium market? A. 1 009 B. 2 341 C. 664 D. 3 350
What is the inverse of the logarithmic function f(x)= log2x.
Solve this equation 3x+5y=262x-y=13

The perimeter of Jonah's square backyard is 56 meters. What is the area of Jonah's backyard?

Answers

If it is a square you would divide the 56 by 4, getting you to where each side equals 14 meters. 14x14=196 meters squared

The diameter of the Sun is approximately 1,400,000 kilometers, while the diameter of Saturn is approximately 1.2 x 105kilometers. How many kilometers larger is the diameter of the Sun than the diameter of Saturn?a) 1.28 times 10 to the sixth power
b) 1.52 times 10 to the sixth power
c) 1.28 times 10 to the seventh power
d) 1.58 times 10 to the seventh power
(Times means multiply since I have no multiplication sign on my computer)