Question

Final grades for a class are approximately Normally distributed with a mean of $76$and a standard deviation of $8$. A professor says that the top$10\%$of the class will receive an A, the next$20\%$a B, the next $40\%$a C, the next $20\%$a D, and the bottom $10\%$an F. What is the approximate maximum grade a student could attain and still receive an F for the course?

$$\begin{gathered} a.70 \\ b.69.27 \\ c.65.75 \\ d.62.84 \\ e.57 \end{gathered}$$

Short answer

The correct option is:

$c.65.75$is the approximate maximum grade a student could attain and still receive an F for the course.

Step-by-step solution

 Step 1: Given information 

We have to tell about the approximate maximum grade a student could attain and still receive an F for the course.

Explanation 

While much information is provided, the inquiry solely concerns the value at which a student will receive an F. (but anything more will be a D). The problem further specifies that anything less than $10\%$will result in an F.

For a mean of $76$and a standard deviation of $1$, we don't have a normal distribution table. The trick is to convert to X using the Z score form after using the standardised normal table.

$\text{Then use}{z}_0=\frac{x_0-\mu }{\sigma }$

Multiply by $8$and add $76$to get the answer.

$x_0=-1.28*8+76\approx 65.75$