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.*

Step 1

Introduction:

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

For a particular value, *X* = *X*_{0}, the cumulative probability is denoted by *P* (*X* ≤ *X*_{0}).

If the value of* P* (*X* ≤ *X*_{0}) is known, the value of *X*_{0} 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* (*X* ≥ *X*0) =0.15. Therefore, *P* (*X* ≤ *X*0) =0.85 or *P...*

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