A recent math test had an average score of 75, with a standard deviation of 10. What percentage of people passed the test (i.e. scored a 70 or higher)?

Question

asked Nov 5, 2023 129k views

1 Answer

Dan Prince · Answer 1 · 2023-11-09T00:10:03+0000

We have to find the z-score at first, then use it to find the percentage of 70 or higher

The rule of the z-score is

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

μ is the mean

σ is the standard deviation

Since the average score is 75, then

$\mu=75$

Since the standard deviation is 10, then

$\sigma=10$

Since we need the percentage of 70, then

Substitute them in the rule above to find z

$\begin{gathered} z=(70-75)/(10) \\ z=-(5)/(10) \\ z=-0.5 \end{gathered}$

Now, we will search in the table for the value of -0.5

The value of -0.5 is 0.30854

Since we need the percentage of 70 or higher, then

$\begin{gathered} P(x\ge70)=1-P(x) \\ P(x\ge70)=1-0.30854 \\ P(x\ge70)=0.69146 \end{gathered}$

Change it to percent

$\begin{gathered} P(x\ge70)=0.69146*100\text{ \%} \\ P(x\ge70)=69.146\text{ \%} \end{gathered}$

The percentage of 70 or higher is about 69.15%