George scored a 62 on his AP World History test and had a z-score of -3.75. Julie is also in the class with George and scored an 83 on the same test, with a z-score of 1.5. From this information, FIND THE CLASS mean and standard deviation.
(62-mean)/st.dev.=-3.75
(83-mean)/st.dev.=1.5
Solve this system.
thanks. my teacher gave me the answer, but i don't know how to get to it. So is this the way to get to the answer
To find the class mean and standard deviation, we can use the z-score formula. The z-score formula is given by:
z = (x - μ) / σ
Where:
- z is the z-score
- x is the individual score
- μ is the population mean
- σ is the population standard deviation
In this case, we have the z-scores of both George and Julie, as well as their individual scores. We can set up two equations using the z-score formula and solve for the mean and standard deviation.
For George:
- x = 62 (his score)
- z = -3.75 (his z-score)
Substituting these values into the z-score formula:
- -3.75 = (62 - μ) / σ
For Julie:
- x = 83 (her score)
- z = 1.5 (her z-score)
Substituting these values into the z-score formula:
- 1.5 = (83 - μ) / σ
Now, we have a system of two equations with two variables (μ and σ). We can solve this system to find the mean (μ) and the standard deviation (σ) of the class.
To solve the system of equations, we can use algebraic methods, such as substitution or elimination. After solving the system, we will obtain the values for the class mean (μ) and the standard deviation (σ).