$MathMaster logo$

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 average weight of a sample of 50 students in kg, given that the mean weight is 65kg, mode is 70kg, median is 67kg, and range is 35kg?

+

What is the sum of the first natural numbers from 1 to 100?

+

Math question: Find the absolute extrema of the function f(x) = x^2 - 3x + 2 on the interval [1, 4].

+

New questions in Mathematics

Pedro bought 9 kg of sugar at the price of R$1.80 per kilogram, six packets of coffee at the price of R$3.90 per packet and 8 kg of rice at the price of R$2.70 per kilogram. Knowing that he paid for the purchases with a R$100.00 bill, how much change did he receive?

String x = 5 Int y=2 System.out.println(x+y)

A food delivery company charges on average a delivery fee of $5 per order (including food and shipping) and has monthly fixed costs of $600. If the average cost of each meal delivered that is revenue for the company is $10 and the company has a monthly profit of $800, how many orders must they deliver per month?

Determine the momentum of a 20 kg body traveling at 20 m/s.

The beta of a company is 1,41 and its cost of equity 18,95%. What is then the market risk premium if the risk free rate is 0,94%? (in %, 2 decimal places)

Estimate the fifth term if the first term is 8 and the common ratio is -1/2

Three squares have a total area of 35.25 𝑐𝑚2 . The larger square has twice the side-length of the middle-sized square. The smaller square has its side length exactly 0.5 cm smaller than the middle-sixed square. Find the side lengths of each of the three squares.

How to do 15 x 3304

Solve the following equation for x in exact form and then find the value to the nearest hundredths (make sure to show your work): 5e3x – 3 = 25

30y - y . y = 144

The two sides of the triangle are 12 cm and 5 cm, and the angle between the sides is 60°. Cover the area of the triangle!

A,B,C and D are the corners of a rectangular building. Find the lengths the diagonals if AB measures 38' - 9" and AD measures 56' - 3"

Which statement best describes the key changes in perspectives on inclusion? An inclusive program must consider the unique experiences of every child and family as well as the child's strengths and needs. There is a shift in thinking about individual programs as "inclusive programs" to thinking about inclusion as something that reflects the cultural influence of the family. There is a greater emphasis on barriers to full participation and the acknowledgement that all children are unique and must be fully and meaningfully engaged in a program. In an inclusive program all participants are accepted by their peers and other members of the community.

find missing measure for triangle area = 48 m square base = 10m heaighy = ? m

there are 500,000 bacteria at the end of a pin point. 1000 bacteria can make a person sick. then bacteria at the tip of a pin point can make 500 people sick. Also, many people do not know that bacteria can (reproduce). Let's say there are 5 bacteria and we leave it for 15 minutes. bacteria will multiply to 10. if left for up to 30 minutes, 20 bacteria will form. if left up to 45 minutes. bacteria will multiply up to 40. every 15 minutes the bacteria will double 2. if you start with five bacteria that reproduce every 15 minutes, how manu bacteria would you have after 12 hours ?

A 20-year old hopes to retire by age 65. To help with future expenses, they invest $6 500 today at an interest rate of 6.4% compounded annually. At age 65, what is the difference between the exact accumulated value and the approximate accumulated value (using the Rule of 72)?

f(r) = 1/r+9 find f(x^2) + 1