Question

Professor Ivy’s students have a Mean grade of 69.5 and a Standard Deviation of 6.5.3. If Johnny has an 82 in the class, what would the z-score for Johnny’s grade be? (round to the tenthsplace)4. What percentile does Johnny’s score put him in? (round to the nearest whole number)

Answer 1

Given:

Mean,ц = 69.5

Standard deviation, σ = 6.5

Let's solve for the following:

• 3. If Johnny has an 82 in the class, what would the z-score for Johnny’s grade be?

Apply the z-score formula:

`z=(x-\mu)/(\sigma)`

Where:

x = 82

ц = 69.5

σ = 6.5

Thus, we have:

`\begin{gathered} z=(82-69.5)/(6.5) \\ \\ z=(12.5)/(6.5) \\ \\ x=1.9 \end{gathered}`

Therefore, the z-score is 1.9

Question 4.

Here, we are to find P(Z<1.9).

Using the standard normal distribution table, we have:

NORMSDIST(1.9) = 0.9712

Now convert to percentage:

0.9712 x 100 = 97.12% = 97%

ANSWER:

3). 1.9

4.) 97%