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An instructor in a large lecture class found, at the end of the semester, that the total point distribution in his class was approximately Normal, with a mean of 530 and a standard deviation of 80. If 10% of the class is to receive A’s (the instructor grades on a curve), what is the lowest number of points that a student can have and still earn an A?

Answer :

Answer: The lowest number of points that a student can have and still earn an A is 632.

Step-by-step explanation:

Since we have given that

Mean = 530

Standard deviation = 80

If 10% of the class is to receive A's, then we need to find the lowest number of points that a student can have and still earn an A.

Let X be the number of points.

so, [tex]P(X\geq x)=0.10[/tex]

so, it becomes,

[tex]P(\dfrac{X-\mu}{\sigma}\geq \dfrac{x-530}{80})=0.10\\\\P(Z\geq \dfrac{x-530}{80})=0.10\\\\P(Z\leq \dfrac{x-530}{80})=1-0.10=0.90[/tex]

From the Z-table, we get that

[tex]P(Z\leq 1.28)=0.90[/tex]

So, we get that

[tex]\dfrac{x-530}{80}=1.28\\\\x-530=1.28\times 80\\\\x-530=102.4\\\\x=102.4+530\\\\x=632.4[/tex]

Hence, the lowest number of points that a student can have and still earn an A is 632.

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