for a population with m=62 and s=12, find the x value that corresponds to esch of the following z-scores: -0.25,-1.50,0.50,2.00
for Z=-0.25, that is .25 std below the mean, or
62 - 0.25*12 = 62-3 = 59
Same for the others.
To find the corresponding x value for each given z-score, you can use the formula:
x = μ + (z * σ)
Where:
x is the corresponding value in the population
μ is the mean of the population
z is the given z-score
σ is the standard deviation of the population
Given:
μ = 62 (mean)
σ = 12 (standard deviation)
For z-score -0.25:
x = 62 + (-0.25 * 12)
x = 62 - 3
x = 59
For z-score -1.50:
x = 62 + (-1.50 * 12)
x = 62 - 18
x = 44
For z-score 0.50:
x = 62 + (0.50 * 12)
x = 62 + 6
x = 68
For z-score 2.00:
x = 62 + (2.00 * 12)
x = 62 + 24
x = 86
Therefore, the corresponding x-values for the given z-scores are:
-0.25 corresponds to x = 59
-1.50 corresponds to x = 44
0.50 corresponds to x = 68
2.00 corresponds to x = 86