2. Let's assume that the number of times that someone is overdue for a bill (credit card, utility, mortgage payment, etc) is distributed normally with a mean of 10 times with a standard deviation of 3.
To calculate the z-score for a specific value, we can use the formula:
z = (x - μ) / σ
Where:
- z is the z-score
- x is the given value
- μ is the mean
- σ is the standard deviation
Let's calculate some z-scores for different overdue amounts:
1. For someone who is overdue 12 times:
z = (12 - 10) / 3
z = 2 / 3
z ≈ 0.67
2. For someone who is overdue 5 times:
z = (5 - 10) / 3
z = -5 / 3
z ≈ -1.67
3. For someone who is overdue 10 times (the mean):
z = (10 - 10) / 3
z = 0 / 3
z = 0
These z-scores tell us the number of standard deviations a given value is from the mean. A positive z-score indicates an overdue amount above the mean, while a negative z-score indicates an amount below the mean. A z-score of 0 means that the value is equal to the mean.