A population has a norma distribution with a mean of 50 and a standard deviation of 10. what is ther standard z-score corresponding to to 70? what is the standard z-score corresponding to 40?
To find the standard z-score for a given value, you need to use the formula:
z = (x - μ) / σ
where:
- z represents the standard z-score
- x is the given value
- μ is the mean of the population
- σ is the standard deviation of the population
In this case, the mean (μ) is 50 and the standard deviation (σ) is 10.
1. To find the standard z-score corresponding to 70:
Substituting the given values into the formula:
z = (70 - 50) / 10
z = 20 / 10
z = 2
So, the standard z-score corresponding to 70 is 2.
2. To find the standard z-score corresponding to 40:
Substituting the given values into the formula:
z = (40 - 50) / 10
z = -10 / 10
z = -1
So, the standard z-score corresponding to 40 is -1.