The mean and SD for a, b and 2 are 3 and 2/root 3 respectively. find the value of ab. pls do show the steps?

Question

Answer

Answer

Answer

Answer

Given:

Mean of a, b, and 2 = 3

Standard deviation of a, b, and 2 = 2/√3

To Find:

Value of ab

Solution:

Let’s assume the data follows a normal distribution.

Step 1: Finding the Variance
Variance of a set of data can be calculated using the formula:

Variance = (Standard Deviation)^2

Variance of a, b, and 2 = (2/√3)^2 = 4/3

Step 2: Forming Equations
We know that the sum of a, b, and 2 is 3. Therefore, we can form two equations as follows:

a + b + 2 = 3 ---(1)
ab = (a + b + 2 - 3)(3 - 2) = (a + b - 1) ---(2)

Step 3: Solving Equations
We can substitute equation (1) in equation (2) and get:

ab = (a + b - 1) = (3 - 2 - 2) = -1

Now, we can substitute the value of ab in equation (1) and get:

a + b + 2 = 3
a + b = 1

Squaring both sides, we get:

(a + b)^2 = 1
a^2 + b^2 + 2ab = 1
Since ab = -1, we can substitute the value and simplify:

a^2 + b^2 - 2 = 1
a^2 + b^2 = 3

Step 4: Solving for a and b
We can solve the above two equations to find the values of a and b:

a + b = 1
a^2 + b^2 = 3

Substituting a = 1 - b in the second equation, we get:

(1 - b)^2 + b^2 = 3
2b^2 - 2b - 2 = 0
b^2 - b - 1 = 0

Solving the quadratic equation, we get:

b = (1 ± √5)/2
a = 1 - b

Therefore, the two possible sets of values for a and b are (a,b) = (-0.618, 1.618) and (a,b) = (1.618, -0.618).

Step 5: Finding the Value of ab
We can substitute the values of a and b in equation (2) and get:

ab = (a + b - 1) = (1.618 + (-0.618) - 1) = -1

Therefore, the value of ab is -1.

Answer:

The value of ab is -1.

Answer

Mis printed
SD = square root of 14/3
answer= 6
a and b= 1 and 6

Similar CA Foundation Doubts

The mean and SD for a, b and 2 are 3 and 2/√3 respectively. The value of ab would be?

The mean and sd for a, b and 2 are 3 and 2/root 3. The value of ab is?

The mean and SD for a,b and 2 are 3 and 2/√3 respectively , the value of ab would be?

The mean and SD for a, b and 2 are 3 and 2/√3 respectively, the value of ab would be?

The mean and sd for a,b and 2 are 3 and 2/√3 respectively,the value oc ab would be?

Top Courses for CA FoundationView all

Quantitative Aptitude for CA Foundation

Principles and Practice of Accounting

Business Laws for CA Foundation

Business Economics for CA Foundation

Mock Tests & Past Year Papers for CA Foundation

Top Courses for CA Foundation

Top Courses for CA Foundation

Suggested Free Tests

Related Content

CA Foundation Courses

Other Courses

How To Prepare?

Other Exams

Company