The 1.5 standard deviations below the mean implies that the Z-score value will be equal to -1.5.
The test score 70 is 1.5 standard deviations below the mean .
We have given that,
The Score standardized test are Normally distributed,
Mean ,μ = 100
Standard deviations, s.d = 20
we have to calculate test score is 1.5 standard deviations below mean.
so, Z- score = -1.5
This is the z-score formula or z-score equation.
Z = (x − μ )/σ
Where, Z--> z-score
x---> the value in question
μ--> mean of the distribution
σ --> standard deviation of the distribution
plugging all known the value in formula
-1.5 = (x- 100)/20
=> -1.5 × 20 = x - 100
=> x = -30 + 100 = 70
So, 70 is the test score that is 1.5 standard deviations from the mean.
To learn more about Z-score , refer :
https://brainly.com/question/24213960
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