Question

The mean of the scores obtained by a class of students on a physics test is 42. The standard deviation is 8%. Students have to score at least 50 to pass the test.
Assuming that the data is normally distributed,  (______%) of the students passed the test.

% of students passed ?
  choices:   5   16   34   58 

Answer 1

The correct answer is:
16%.

Explanation:
We use a z-score to answer this question.
The formula for a z-score is:
 z=$\frac{x-mue}{sigma}$,
where mue is the mean and sigma is the standard deviation.

Using our information, we have:
z=$\frac{50-42}{8} = \frac{8}{8} = 1$.

Using a z-table, we see that the area to the left of, or less than, this score is 0.8413. We want to know how many students scored more than this, so we subtract from 1:
1-0.8413=0.1587, which rounds to 16%.

Answer 2

Answer:

B. 16%.

Step-by-step explanation:

We have been given that the The mean of the scores obtained by a class of students on a physics test is 42. The standard deviation is 8%. Students have to score at least 50 to pass the test.

First of all, we will find z-score of sample score 50 by using z-score formula.

$z=\frac{x-\mu}{\sigma}$, where,

$z=\text{z-score}$,

$x=\text{Sample score}$,

$\mu=\text{Mean}$,

$\sigma=\text{Standard deviation}$.

Upon substituting our given values in z-score formula we will get,

$z=\frac{50-42}{8}$

$z=\frac{8}{8}$

$z=1$

Now, we will use normal distribution table to find the area above the z-score of 1.

Using normal distribution table we will get,

$P(z>1)=1-P(z$

$P(z>1)=1-0.84134$

$P(z>1)=0.15866$

Now we will multiply our answer by 100 to convert it into percentage.

$0.15866\times 100\%=15.866\%\approx 16\%$

Therefore, approximately 16% of the students passed the test and option B is the correct choice.