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Answer :
Application acceptance requires a minimum score of 392, which is required.
How to calculated the minimal score for admission?
Make "x" the required minimum score.
Given:
The average score is 500.
Standard deviation () is equal to 100
Admission percentage, P > 86 percent, or 0.86
Thus, the area under the normal distribution curve to the right of the z-score, which is 86%, is provided.
The portion of the score left over is displayed in the z-score table. As a result, we will calculate the z-score value for area as 100 - 86 = 14% or 0.14.
The z-score is therefore equal to -1.08 for value of 0.1401.
P(x>x0) = P(z > -1.08)
= -1.08 = x0 - 500 /100
x0 - 500 = -1.08 × 100
x0 = -1.08 + 500 = 392.
As a result, 392 is the minimal score needed for admission.
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