$MathMaster logo$

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

85 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)

Question: Simplify the mixed number 3 and 1/4 + 2 and 3/5, factorize the sum, and find the largest real factor.

+

What is the equation of the line passing through points (2, 5) and (4, 10)?

+

What is 36% written as a decimal?

+

New questions in Mathematics

Using a remarkable product you must factor the expression: f(x) =36x^2-324 and you are entitled to 5 steps

If we have the sequence: 3, 6, 12, 24 Please determine the 14th term.

The Lenovo company manufactures laptop computers, it is known that for every 60 laptops produced, 54 go on the market with the highest quality standards. If a sample of 15 laptops is taken, calculate the probability that: Exactly 2 are not of high quality

A soft drink machine outputs a mean of 23 ounces per cup. The machines output is normally distributed with a standard deviation of 3 ounces. What is the probability of filling a cup between 26 and 28 ounces round your answer to four decimal places

(2x+5)^3+(x-3)(x+3)

"If three wolves catch three rabbits in three hours, how many wolves would it take to catch a hundred rabbits in a hundred hours?" The answer is the number of response units.

The actual length of an object is 1.3 m . If the blueprint uses a scale of 1 : 12 , what is the length of the line on the drawing?

A pair of die is thrown and the absolute difference of the two scores is recorded. What is the probability of the absolute difference being 4 or more?

You are the newly appointed transport manager for Super Trucking (Pty) Ltd, which operates as a logistics service provider for various industries throughout southern Africa. One of these vehicles is a 4x2 Rigid Truck and drawbar trailer that covers 48,000 km per year. Use the assumptions below to answer the following questions (show all calculations): Overheads R 176,200 Cost of capital (% of purchase price per annum) 11.25% Annual License Fees—Truck R 16,100 Driver Monthly cost R 18,700 Assistant Monthly cost R 10,500 Purchase price: - Truck R 1,130,000 Depreciation: straight line method Truck residual value 25% Truck economic life (years) 5 Purchase price: Trailer R 370,000 Tyre usage and cost (c/km) 127 Trailer residual value 0% Trailer economic life (years) 10 Annual License Fees—Trailer R 7,700 Fuel consumption (liters/100km) 22 Fuel price (c/liter) 2053 Insurance (% of cost price) 7.5% Maintenance cost (c/km) 105 Distance travelled per year (km) 48000 Truck (tyres) 6 Trailer (tyres) 8 New tyre price (each) R 13,400 Lubricants (% of fuel cost) 2.5% Working weeks 50 Working days 5 days / week Profit margin 25% VAT 15% Q1. Calculate the annual total vehicle costs (TVC)

The maximum gauge pressure of a hydraulic ramp is 16 atm, with a support area whose diameter is 20 cm. What is the mass of the heaviest vehicle that can be lifted?

A vaccine has a 90% probability of being effective in preventing a certain disease. The probability of getting the disease if a person is not vaccinated is 50%. In a certain geographic region, 60% of the people get vaccinated. If a person is selected at random from this region, find the probability that he or she will contract the disease. (4 Points)

Let v be the set of all ordered pairs of real numbers and consider the scalar addition and multiplication operations defined by: u+v=(x,y)+(s,t)=(x+s+1,y+t -two) au=a.(x,y)=(ax+a-1,ay-2a+2) It is known that this set with the operations defined above is a vector space. A) calculate u+v is au for u=(-2,3),v=(1,-2) and a=2 B) show that (0,0) #0 Suggestion find a vector W such that u+w=u C) who is the vector -u D) show that axiom A4 holds:-u+u=0

Two minus log 3X equals log (X over 12)

How do you convert a fraction to a decimal

The average weekly earnings in the leisure and hospitality industry group for a re‐ cent year was $273. A random sample of 40 workers showed weekly average ear‐ nings of $285 with the population standard deviation equal to 58. At the 0.05 level of significance can it be concluded that the mean differs from $273? Find a 95% con‐ fidence interval for the weekly earnings and show that it supports the results of the hypothesis test.

-6 - t / 4 = -1

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?