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
Basile [38]
2 years ago
12

5. Based on recent results, scores on the SAT test are normally distributed with a mean of 1511 and a standard deviation of 312.

Scores on the ACT test are normally distributed with a mean of 21.1 and a standard deviation of 5.1. Assume that the two tests use different scales to measure the same aptitude. If someone gets an SAT score that is in the 95th percentile, find the actual SAT score and the equivalent ACT score.
Mathematics
1 answer:
Mekhanik [1.2K]2 years ago
5 0

Answer:

The actual SAT score is 2024.

The equivalent ACT score is 29.49.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

SAT score that is in the 95th percentile

Scores on the SAT test are normally distributed with a mean of 1511 and a standard deviation of 312, which means that \mu = 1511, \sigma = 312

95th percentile is X when Z has a pvalue of 0.95, so X when Z = 1.645. The score is:

Z = \frac{X - \mu}{\sigma}

1.645 = \frac{X - 1511}{312}

X - 1511 = 1.645*312

X = 2024

The actual SAT score is 2024.

Equivalent ACT score:

The equivalent ACT score is the 95th percentile of ACT scores.

Scores on the ACT test are normally distributed with a mean of 21.1 and a standard deviation of 5.1, which means that \mu = 21.1, \sigma = 5.1. So

Z = \frac{X - \mu}{\sigma}

1.645 = \frac{X - 21.1}{5.1}

X - 21.1 = 1.645*5.1

X = 29.49

The equivalent ACT score is 29.49.

You might be interested in
Simplify the expression by combining like terms<br> 2v + 6 + 4v + 8 + v
harkovskaia [24]

7v + 14

(2v + 4v + v) + (6 + 8)

7v + 14

5 0
3 years ago
Read 2 more answers
Please<br> Help !!!!!!!!!!!
slava [35]

Answer:

Painting USA is cheaper. They cost $700 dollars. The other place costs $1,000 dollars

7 0
3 years ago
Complete the statement.
mario62 [17]

Answer:

B

Step-by-step explanation:

edg 2020

8 0
2 years ago
Read 2 more answers
How can I solve this?
jok3333 [9.3K]

The 3 inside angles need to equal 180 degrees.

Angle K is given as 48 degrees.

Angle M would be 90 degrees.

Angle J = 180 - 90 - 48 = 42

Angle J = 42 degrees

3 0
2 years ago
2 and 1/4 cups equals how many pints? WILL MARK BRAINILEST!!! IF CORRECT
Mumz [18]
The answer is 1.125 liquid pints
7 0
3 years ago
Other questions:
  • Z is centroid of triangle RST. What is RW, if RV=4x+3, WS=5x-1, and VT=2x+9?
    6·1 answer
  • This is my little brothers HW and I don't get it lol plz help
    5·2 answers
  • PLEASE I'm DESPERATE!. Find a, b, c, and d such that the cubic . f(x) = ax3 + bx2 + cx + d. satisfies the given conditions.. Rel
    15·2 answers
  • Find the measure of angle x. Round your answer to the nearest hundredth. (please type the numerical answer only)
    11·1 answer
  • 2x + y + 3z = 19<br> 3x + 2y + 3z = 19<br> X + 4y + 2z = 9<br> What is the value of x?
    13·2 answers
  • A clown sells large balloon animals for $25 each. Small balloon animals sell for $10 each. Jordan is buying 2 large balloon anim
    11·1 answer
  • Solve for EG. A) 18 B) 12 9 D) 6​
    6·2 answers
  • WILL GIVE BRAINLIEST, ANSWER ONE OR BOTH I DONT CARE JUST PLSSS HELP
    15·1 answer
  • A rectangle field is 10m longer than its width. If the perimeter is 300cm, find;
    15·1 answer
  • Four glasses of milk and 3 snack bars have a total of 82 carbohydrates (carbs), and 2 glasses of milk and 4 snack bars have a to
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!