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Answer:
The minimum score an applicant must receive for admission is 392.
Step-by-step explanation:
Let the minimum score required be 'x₀'.
Given:
Mean score (μ) = 500
Standard deviation (σ) = 100
Percentage required for admission, P > 86% or 0.86
So, we are given the area under the normal distribution curve to the right of z-score which is 86%.
The z-score table gives the area left of the z-score value. So, we will find the z-score value for area 100 - 86 = 14% or 0.14
So, for value equal to 0.1401, the z-score = -1.08
Now,
So, we find x₀ using the formula of z-score which is given as:
Therefore, the minimum score an applicant must receive for admission is 392.