$MathMaster logo$

MathMaster

Home
general
scores on a test have mean 70 and standard deviation 15 let x denote a student s score on this test the professor wants to

Question

Scores on a test have mean 70 and standard deviation 15. Let x denote a student’s score on this test. The professor wants to adjust the scores so that they have mean 75 and standard deviation 12. Let y denote a student’s adjusted score. y is related to x by y = a + bx, and the professor wants to find a and b so that the adjusted scores have the correct mean and standard deviation. What does a have to be?

110

likes

551 views

Answer to a math question Scores on a test have mean 70 and standard deviation 15. Let x denote a student’s score on this test. The professor wants to adjust the scores so that they have mean 75 and standard deviation 12. Let y denote a student’s adjusted score. y is related to x by y = a + bx, and the professor wants to find a and b so that the adjusted scores have the correct mean and standard deviation. What does a have to be?

$Expert avatar$

4.4

92 Answers

E(a+bX)=75

E(a)+bE(X)=75

a+70b=75

70b=75-a and Var(a+bX)=12^2

b^2Var(X)=144

b^2(15)^2=144

b^2=\frac{144}{225}

b=\frac{12}{15}

b=\frac{4}{5} then 70b=75-a

56=75-a

a=19 therefore, a=19 and b=\frac{4}{5}

Frequently asked questions (FAQs)

What is the range of the tangent function for angles from 0 to 360 degrees?

+

Math Question: What is the positive integer solution to the equation a^n + b^n = c^n (where n>2) according to Fermat’s Theorem?

+

Question: Can you factor the expression 3x^2 - 7x - 6 using the distributive property?

+

New questions in Mathematics

Let the vectors be u=(-1,0,2) , v=(0,2,-3) , w=(2,2,3) Calculate the following expressions a)<u,w> b) <2u- 5v,3w>

what is 9% of 307

For a temperature range between 177 degrees Celsius to 213 degrees Celsius, what is the temperature range in degrees Fahrenheit.

Use the elimination to find the solution to each linear system. X+y=43 2x-y=20

what is the annual rate on $525 at 0.046% per day for 3 months?

The points (-5,-4) and (3,6) are the ends of the diameter of the circle calculate subequation

X~N(2.6,1.44). find the P(X<3.1)

Translate to an equation and solve. Let x be the unknown number: What number is 52% of 81.

The annual real property tax liability for a residential property is $4302 and has been paid by the seller in advance of closing. Using the 30-day month/260-day year method what will be the tax proration entry on the settlement statement round to the nearest dollar for a closing on Oct. 26 if the buyer owns the day of closing? a. $3525 credit to the buyer and $777 debit to the seller b. $777 debit to the buyer and $3525 debit to the seller c. $777 credit to the buyer and $777 debit to the seller d. $3525 debit to the buyer and $3525 credit to the seller *Can anyone help with this? I am studying for my real estate exam and am having trouble with some of the calculations :)

Calculate the area of the parallelogram with adjacent vertices (1,4, −2), (−3,1,6) 𝑦 (1, −2,3)

A property sold for $745,000 in a co-brokered transaction. The seller has agreed to pay a 7% commission to the listing firm. The listing firm has agreed to equally split the commission with the selling firm. If the buyer’s broker will receive 8% of the selling firm’s commission, how much commission will the buyer’s broker receive? $14,900 $3725 $$37250 $18625

solve R the following equation 4 x squared - 35 - 9 over x squared is equal to 0

25) Paulo saves R$250.00 per month and keeps the money in a safe in his own home. At the end of 12 months, deposit the total saved into the savings account. Consider that, each year, deposits are always carried out on the same day and month; the annual yield on the savings account is 7%; and, the yield total is obtained by the interest compounding process. So, the amount that Paulo will have in his savings account after 3 years, from the moment you started saving part of your money monthly, it will be A) R$6,644.70. B) R$ 9,210.00. C) R$ 9,644.70. D) R$ 10,319.83. E) R$ 13,319.83

Emile organizes a community dance to raise funds. In addition to paying $300 to rent the room, she must rent chairs at $2 each. The quantity of chairs rented will be equal to the number of tickets sold. She sells tickets for $7 each. How much should she sell to raise money?

Let f(x)=-1/2x+5 evaluate f(-6)