The average of 2 number is 20 and their standard deviation 5. Find the two numbers?

Question

Answer

Problem:

The average of 2 numbers is 20 and their standard deviation is 5. Find the two numbers?

Solution:

To solve this problem, we need to use the formula for the mean and standard deviation of a sample:

Mean: The sum of all the values divided by the number of values

Standard Deviation: The square root of the sum of the squared differences between each value and the mean, divided by the number of values minus 1

Step 1:

Let's assume the two numbers to be x and y. We know that:

The average of the two numbers is 20

The standard deviation of the two numbers is 5

Using the formula for mean, we can write:

(x + y) / 2 = 20

Step 2:

Next, we can use the formula for standard deviation to write:

sqrt(((x - 20)^2 + (y - 20)^2) / 2) = 5

Step 3:

We can simplify the equation from step 2:

((x - 20)^2 + (y - 20)^2) / 2 = 25

Step 4:

Now, we have two equations from steps 1 and 3:

(x + y) / 2 = 20

((x - 20)^2 + (y - 20)^2) / 2 = 25

Using algebra, we can solve for x and y. One way to do this is to solve for y in the first equation and substitute it into the second equation:

y = 40 - x

((x - 20)^2 + (40 - x - 20)^2) / 2 = 25

Step 5:

We can simplify the equation from step 4:

((x - 20)^2 + (20 - x)^2) / 2 = 25

(x - 20)^2 + (20 - x)^2 = 50

Step 6:

We can expand the equation from step 5:

2x^2 - 80x + 800 = 50

2x^2 - 80x + 750 = 0

Step 7:

Now, we can use the quadratic formula to solve for x:

x = (80 ± sqrt(80

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