Suppose x, the grade on a midterm exam, is normally distributed with mean 70 and standard deviation 10 The instructor wants to give 15% of the class an A. What cutoff should the instructor use to determine who gets an AFurther suppose that the instructor wants to give 10% of the class an A−. What cutoff should the instructor use to determine who gets an A−*Please do not solve using Microsoft Excel.  My professor is not teaching using excel.  I would like to see the steps involved to solving the problem for my own study reference for exams.*

Question
Asked Nov 9, 2019

Suppose x, the grade on a midterm exam, is normally distributed with mean 70 and standard deviation 10

 

The instructor wants to give 15% of the class an A. What cutoff should the instructor use to determine who gets an A

Further suppose that the instructor wants to give 10% of the class an A−. What cutoff should the instructor use to determine who gets an A−

*Please do not solve using Microsoft Excel.  My professor is not teaching using excel.  I would like to see the steps involved to solving the problem for my own study reference for exams.*

 

 

 

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Expert Answer

Step 1

Introduction:

Suppose the normally distributed random variable, X, has mean, μ and standard deviation, σ.

For a particular value, X = X0, the cumulative probability is denoted by P (XX0).

If the value of P (XX0) is known, the value of X0 can be uniquely found using inverse cumulative function, either by standardization and then taking the help of a standard normal table, or by using relevant software.

Step 2

Calculation:

The random variable x denotes the grade on the midterm exam. It is given that x is normally distributed with mean 70 and standard deviation 10. The instructor wants to give 15% of the class an A. That is,   P (XX0) =0.15. Therefore, P (XX0) =0.85 or P...

Cutoff uzxo
= 70 +1.04x10
= 70 +10.4
= 80.4
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Cutoff uzxo = 70 +1.04x10 = 70 +10.4 = 80.4

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