Question

Statistics. Hi! I need the answer for this:The latest math quiz had an average score of 83.2 with a standard deviation of 3.4. What percent of students scored between a 79.8 and 86.6?

Answer 1

Answer:

$68.27\text{ \%}$

Explanation:

Here, we want to get the percentage of students that scored between the two scores

To get this, we need the z-scores of the given scores

Mathematically, we can calculate the z-scores as follows:

$\begin{gathered} z\text{ = }\frac{x-\mu}{\sigma} \\ \\ \mu\text{ = mean = 83.2} \\ \sigma\text{ = standard deviation = 3.4} \end{gathered}$

Now, we calculate the z-score for each of the scores. We call the first z1 and the second z2

We proceed as follows:

$z_1=\frac{79.8-83.2}{3.4}\text{ = -1}$

For the second score, we have:

$z_2\text{ = }\frac{86.6-83.2}{3.4}\text{ = 1}$

Finally, what we have to do is to find the probability between the two z-scores

We have this as follows:

[tex]P\mleft(-1The values of the z-score are obtained from the probability distribution table