Given the following information about a sample, calculate a z score for a test grade of 91.
= 87, s = 4.01
I assume the median is 87
z-score = (91-87)/4.01
= ....
Why did the test grade go to the circus? Because it wanted to join the z-scored circus!
But in all seriousness, let's calculate the z-score. The z-score formula is:
z = (x - μ) / σ
Where:
- x is the value you want to standardize (in this case, the test grade of 91)
- μ is the mean (average) of the sample (in this case, 87)
- σ is the standard deviation of the sample (in this case, 4.01)
Plugging in the values:
z = (91 - 87) / 4.01
Calculating:
z = 4 / 4.01
z ≈ 0.998 (rounded to three decimal places)
So the z-score for a test grade of 91 is approximately 0.998.
To calculate the z-score, we'll use the formula:
z = (x - μ) / σ
Where:
x = the value we want to calculate the z-score for (test grade of 91)
μ = the mean of the sample (given as 87)
σ = the standard deviation of the sample (given as 4.01)
Plugging in these values into the formula, we get:
z = (91 - 87) / 4.01
Simplifying this expression, we have:
z = 4 / 4.01
Calculating this further, we get:
z ≈ 0.99750623
Therefore, the z-score for a test grade of 91, given the sample mean of 87 and standard deviation of 4.01, is approximately 0.9975.
To calculate the z-score for a test grade of 91, you will need the mean (µ) and the standard deviation (σ) of the sample.
In this case, you are given the mean (µ) = 87 and the standard deviation (σ) = 4.01.
The formula to calculate the z-score is:
z = (X - µ) / σ
where X is the given value, µ is the mean, and σ is the standard deviation.
Now, let's substitute the values into the formula:
z = (91 - 87) / 4.01
z = 4 / 4.01
z ≈ 0.997
Therefore, the z-score for a test grade of 91, given a mean of 87 and a standard deviation of 4.01, is approximately 0.997.