1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
suter [353]
2 years ago
10

Suppose that scores on a knowledge test are normally distributed with a mean of 60 and a standard deviation of 4.3. Scores on an

aptitude test are normally distributed with a mean of 110 and a standard deviation of 7.1.
Boris scored a 57 on the knowledge test and 106 on the aptitude test. Callie scored 63 on the knowledge test and 114 on the aptitude test.


(a) Which test did Boris perform better on? Use z-scores to support your answer.

(b) Which test did Callie perform better on? Use z-scores to support your answer.

(c) Boris also took a logic test. His z-score on that test was . Does this change the answer to which test Boris performed better on? Explain your answer using z-scores.
Mathematics
1 answer:
Sphinxa [80]2 years ago
6 0

Question:

(c) Boris also took a logic test. His z-score on that test was +0.93 . Does this change the answer to which test Boris performed better on? Explain your answer using z-scores.

Answer:

The answers to the questions are;

(a) Based on the z score, Boris perform better on his aptitude test.

(b) Based on the z score, Callie perform better on his knowledge test .

(c) For Boris since +0.93 = z_{logic} >  z_{knowledge}  >  z_{aptitude}

Yes as Boris now performed best on the logic test.

Step-by-step explanation:

The z-score of a score is a measurement of the score withe respect to its distance from the mean as a factor of the standard deviation.

To solve the question, we note that we are required to find the z score as follows.

z score is given by z = \frac{x -\mu}{\sigma}

Where:

z = Standard score

x = Score

σ = Standard deviation

μ = Mean

(a) To find out which test did Boris performed better usin z score, we have

Boris scored a

57 on the knowledge test and

106 on the aptitude test

Therefore the z sore for the knowledge test is

z = \frac{x -\mu}{\sigma}

Here

x = 57

μ = 60

σ = 4.3

Therefore

z_{knowledge} = \frac{57 -60}{4.3} = -3/4.3 = -30/43 = -0.6977

The z sore for Boris on the aptitude test is

Here

x = 106

μ = 110

σ = 7.1

z_{aptitude} = \frac{106 -110}{7.1} = -40/17 = -0.5634

Based on the z score, Boris perform better on the aptitude test as his z score is higher (on the number line), --0.5634, compared to the z score on the knowledge test , -0.6977

(b) For Callie we have

Callie scored a

63 on the knowledge test and

114 on the aptitude test

Therefore the z sore for the knowledge test is

z = \frac{x -\mu}{\sigma}

Here

x = 63

μ = 60

σ = 4.3

Therefore

z_{knowledge} = \frac{63 -60}{4.3} = 3/4.3 = 30/43 = 0.6977

The z sore for Callie on the aptitude test is

Here

x = 114

μ = 110

σ = 7.1

z_{aptitude} = \frac{114 -110}{7.1} = 40/17 = 0.5634

Based on the z score, Callie perform better on the knowledge test as his z score is higher (on the number line), 0.6977, compared to the z score on the aptitude test , 0.5634.  

(c) If z_{logic}  = +0.93 then sinc for Boris z_{knowledge} = -0.6977 and

z_{aptitude}=  - 0.5634 then

z_{logic} >  z_{knowledge}  >  z_{aptitude}

Therefore Boris now performed best on the logic test.

You might be interested in
How to simply 11/20 in fraction form
Rus_ich [418]
The answer to the question is .55. The line is a division sign, so all you need to do is divide the top number by the bottom number.
7 0
2 years ago
Read 2 more answers
X+4y=4 in slope intercept form
MAXImum [283]

Answer:

Slope: −14y-intercept: (0,1)

Step-by-step explanation:

7 0
2 years ago
HELP ASAP! BEING TIMED!
Sloan [31]

Answer:

7

Step-by-step explanation:

that what i thank it is

6 0
3 years ago
Read 2 more answers
Write the equation of a line that passes through points (-3,2)(-9,-8)
ollegr [7]

Answer:

slope intercept form is y=x+1

6 0
2 years ago
Marcus spent 3.25$ to wash his car. If one querter operates the car wash 60 seconds hiw long did it take him to wash his car.
ddd [48]

Answer:

answer=answer

Step-by-step explanation:

Y E S

I love simple math.

3.25$ to wash the car.

60 seconds: 1 quarter

how many quarters is 3.25?

4 quarters per dollar. so it'd be 13 quarters, then do 13*60=how many seconds u got. 780 seconds. I think you can do 780/60

HINT: hey, psst, it's 13 minutes. : D

HEY DOn'T teLL tHeM tHe ANSWER. :V

6 0
3 years ago
Other questions:
  • 3 times of 4 yards 2 foot
    11·1 answer
  • One box of cereal is 20 ounces and cost $3. A smaller box of the same type of cereal is 12 ounces and costs $2. Which box of cer
    6·2 answers
  • PLEASE HELP! What is the length of side BC?
    7·1 answer
  • Is (fg)(0)=(f/g)(0)? Explain
    15·2 answers
  • Hi is this true or false? Help?
    8·1 answer
  • LOT OF POINTS AND BRAINLIEST IF YOU'RE RIGHT:
    11·1 answer
  • Order of operation with Integers
    10·1 answer
  • Find the measure of each angle indicated.
    14·1 answer
  • A cyclist rides his bike at a rate of 18 miles per hour. What is this rate in kilometers per hour? How many kilometers will the
    5·2 answers
  • 4. In a scale-drawing blueprint of a house, 1/4of an inch represents 1 foot. If a room in the house has
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!