Respuesta :
If the test scores are normally distributed then the exam score corresponding to a standard score of -0.95 is 83.15 .
In the question ,
it is given that ,
the mean of the normally distributed score is (μ) = 86 ;
the standard deviation of the normally distributed is(σ) = 3 ;
we have to find the exam score(z score) corresponding to the standard score of -0.95 .
we know that z-score for the population mean (μ) and standard deviation(σ) is
Z = (x - μ)/σ
rewriting ,
we get ,
x = μ + Zσ
given that standard score (z) is = -0.95 .
the exam score corresponding to z = -0.95 can be calculated using the formula ,
x = μ + Zσ
Substituting Z = -0.95 , μ = 86 and σ = 3 ;
we get ,
x = 86 + (-0.95)×3
x = 86 - 2.85
x = 83.15
Therefore , the exam score corresponding to the standard score of "-0.95" is 83.15 .
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