Question

On a test that has a normal distribution, a score of 41 falls three standard deviation below the mean, and a score of 73folle one standard deviation above the moon. Determine the mean of the test.

Answer 1

Explanation:

let's denote the mean of the test by u. We know that a score of 41 falls three standard deviations below the mean, and a score of 73 falls one standard deviation above the mean.

From the first statement, we have:

41 = u-3o

where o is the standard deviation.

From the second statement, we have:

73 = u + o

Now we can use these two equations to solve for u. We can start by solving for o and the first equation:

41 = u -3o

41 - u = -3o

o = (u - 41) /3

We can substitute this expression for o into the second equation:

73 = u + o

73 = u + (u - 41 ) / 3

219 = 3u + u - 41

260 = 4u

u = 65

Therefore, the mean of the test is 65.

Answer 2

On a test that has a normal distribution, a score of 41 falls three standard deviation below the mean, and a score of 73

folle one standard deviation above the moon. Determine the mean of the test.

we know that

3=(mean-41)standard deviation -------> first equation

1=(73-mean)/standard deviation ------> second equation

solve the system of equations

Isolate deviation standard

sd=(mean-41)/3

sd=73-mean

73-mean=(mean-41)/3

219-3mean=mean-41

3mean+mean=219+41

4 mean=178

mean=44.5