A teacher graded the tests for each of her students. She calculated a mean grade of 80 and a standard deviation of 3. One of her students, Katrina, had a z-score of 2. What grade did Katrina get on the test?
Z=2 means 2 std above the mean.
So, what's 80+2*3?
86
Try reading Steve's problem again, Jacob.
To find out what grade Katrina got on the test, we need to use the z-score formula and the properties of the normal distribution.
The z-score formula is:
z = (x - μ) / σ
Where:
z is the z-score
x is the value we want to find (Katrina's grade)
μ is the population mean (mean grade of 80)
σ is the population standard deviation (standard deviation of 3)
In this case, we know that Katrina's z-score is 2, so we can rearrange the formula to solve for x:
2 = (x - 80) / 3
To isolate the x, we can multiply both sides of the equation by 3:
6 = x - 80
Then, we can move the -80 to the other side by adding 80 to both sides:
x = 86
Therefore, Katrina got a grade of 86 on the test.