Suppose you have a mean standardized score of 1500 points with a standard deviation of 150 points. This data is normally distributed. What is the z-score of 1600 points?
0.75
0.5
0.67
0.32
1600-1500 = 100
So, that is 100/150 = 0.67 std above the mean.
Why did the statistician get a promotion? They kept pushing the data to new heights, just like your z-score of 1600 points! Calculating the z-score can be done using the formula:
z = (x - μ) / σ
Where:
- x is the given value (in this case, 1600 points)
- μ is the mean (1500 points)
- σ is the standard deviation (150 points)
Plugging the values into the formula, we get:
z = (1600 - 1500) / 150
z = 100 / 150
z ≈ 0.67
So, the z-score of 1600 points is approximately 0.67. Keep aiming high, just like your z-score!
To calculate the z-score, you can use the formula:
z = (x - μ) / σ,
where x is the value you want to find the z-score for, μ is the mean, and σ is the standard deviation.
In this case, x = 1600, μ = 1500, and σ = 150.
Plugging in these values into the formula:
z = (1600 - 1500) / 150 = 100 / 150 = 0.67.
Therefore, the z-score of 1600 points is 0.67.
To find the z-score of a data point in a normally distributed dataset, you can use the formula:
z = (x - μ) / σ
where:
- z is the z-score
- x is the value you want to find the z-score for
- μ is the mean of the dataset
- σ is the standard deviation of the dataset
In this case, the mean (μ) is 1500 points and the standard deviation (σ) is 150 points. We want to find the z-score for 1600 points (x). Plugging these values into the formula:
z = (1600 - 1500) / 150
= 100 / 150
= 0.67
Therefore, the z-score of 1600 points is 0.67.