On his midterm exam, Jimmy scored 75
points, which was exactly 2 standard
deviations above the mean. If the
standard deviation for the test is 4, what is
the mean for the test?
Standard deviation = 4
Two standard deviations = 8
75 - 8 = ?
This will be your mean.
67
To find the mean for the test, we need to determine the value of the mean given that Jimmy scored 75 points, which is 2 standard deviations above the mean.
Given:
Standard deviation (σ) = 4
Jimmy's score (x) = 75
Number of standard deviations (z) = 2
The formula for calculating z-score is:
z = (x - μ) / σ
Where:
z = number of standard deviations from the mean
x = observed value
μ = mean
σ = standard deviation
Rearranging the formula to solve for the mean (μ), we have:
μ = x - z * σ
Now, substituting the given values into the formula:
μ = 75 - 2 * 4
Calculating:
μ = 75 - 8
The mean for the test is:
μ = 67.
To find the mean for the test, we need to use the given information that Jimmy's score is exactly 2 standard deviations above the mean.
Let's denote the mean as μ (mu) and the standard deviation as σ (sigma).
We know that Jimmy's score is 2 standard deviations above the mean:
75 = μ + 2σ
We are also given the standard deviation, which is 4:
σ = 4
Substituting the value of σ in the first equation, we have:
75 = μ + 2(4)
75 = μ + 8
Subtracting 8 from both sides of the equation, we get:
μ = 75 - 8
μ = 67
Therefore, the mean for the test is 67.