At a local high school, GPA's are normally distributed with a mean of 2.9 and standard deviation of 0.6.
x=4.25 is the GPA highest 2.5% of the students.
We have to find the GPA of the highest 2.5% of the students.
Mean = μ = 2.9
Standard deviation = σ = 0.6
Finding the z value for corresponding area 0.9750
For 95% confidence interval ,
z = 1.96
For 97.5% confidence interval,
We get z = 2.25
From
Z = ( x - μ ) / σ
For 2.5% of the students
To solve for x
x = Z*σ + μ
x = 2.25*0.6 + 2.9
x = 1.35 + 2.9
x = 4.25 GPA of highest 2.5% of students
Hence the answer is, x=4.25 is the GPA highest 2.5% of the students.
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