For a population with µ = 70 and ó = 20, find the z-score that corresponds to each of the following X-values
Use z-score formula:
z = (x - mean)/sd
mean = 70
sd = 20
Substitute the values you have into the formula to find z-scores.
To find the z-score corresponding to a given X-value, you can use the formula:
z = (X - µ) / σ
where z is the z-score, X is the given X-value, µ is the population mean, and σ is the population standard deviation.
Given that the population mean (µ) is 70 and the population standard deviation (σ) is 20, let's find the z-score for each of the following X-values:
1) X = 85:
z = (85 - 70) / 20
z = 15 / 20
z = 0.75
Therefore, for X = 85, the corresponding z-score is 0.75.
2) X = 55:
z = (55 - 70) / 20
z = -15 / 20
z = -0.75
Therefore, for X = 55, the corresponding z-score is -0.75.
3) X = 100:
z = (100 - 70) / 20
z = 30 / 20
z = 1.5
Therefore, for X = 100, the corresponding z-score is 1.5.
I hope this helps! Let me know if you have any further questions.
To find the z-score that corresponds to each X-value, you can use the formula:
z = (X - µ) / σ
where:
- z is the z-score
- X is the value from the population
- µ is the mean of the population
- σ is the standard deviation of the population
Let's calculate the z-score for each X-value:
1. X = 80:
z = (80 - 70) / 20
z = 10 / 20
z = 0.5
Therefore, the z-score corresponding to X = 80 is 0.5.
2. X = 60:
z = (60 - 70) / 20
z = -10 / 20
z = -0.5
Therefore, the z-score corresponding to X = 60 is -0.5.
By using this formula, you can calculate the z-score for any X-value in a population with known mean and standard deviation.