If a data set has a mean of 10.0 seconds and a standard deviation of 2.0 seconds, what is the Z score corresponding to the time of 4.0 seconds?
z score= (10-4)/2=3.0
Z score = (score-mean)/SD = (4-10)/2 = -3
To find the Z score corresponding to a given value, you can use the formula:
Z = (X - μ) / σ
where:
Z is the Z score,
X is the value,
μ is the mean, and
σ is the standard deviation.
In this case, the given values are:
X = 4.0 seconds
μ = 10.0 seconds
σ = 2.0 seconds
Plugging these values into the formula, we get:
Z = (4.0 - 10.0) / 2.0
Now let's calculate the Z score:
Z = -6.0 / 2.0
Z = -3.0
Therefore, the Z score corresponding to the time of 4.0 seconds is -3.0.
To calculate the Z-score, you need to use the formula:
Z = (X - μ) / σ
Where:
Z is the Z-score
X is the value you want to calculate the Z-score for
μ is the mean of the dataset
σ is the standard deviation of the dataset
In this case:
X = 4.0 seconds
μ = 10.0 seconds
σ = 2.0 seconds
Plugging these values into the formula, we can calculate the Z-score:
Z = (4.0 - 10.0) / 2.0
Z = -6.0 / 2.0
Z = -3.0
So the Z-score corresponding to the time of 4.0 seconds is -3.0.