Answer to Question #201567 in Statistics and Probability for darshan

Question

In an exam taken by 800 candidates, the average and standard deviation of marks obtained (normally distributed) are 40% and 10% respectively. What should be the minimum score if 350 candidates are to be declared as passed

Answer 1

If it is known that 350 candidates are to be passed then the probability of passing will be equal to $\dfrac{350}{500}=0.70$

If we have $z_1$ is the minimum cut of mark then we can note the following.

$P(z\geq z_1)=0.7=0.5+0.2=P(0<z<\infty)+P(0<z<0.525)=P(z\geq -0.525)$

From the formula we can write the following

$$z_1=-0.525$$

Then we can substitute into the formula.

$$z_1=\dfrac{x-\mu}{\sigma}\\\ \\-0.525=\dfrac{x-40}{10}$$

Now, we can simplify the obtained equations by multiplying on 10 both the sides of the equation:

$$x-40=-5.25\\x=40-5.25\\x=34.75\approx 35\%$$

Finally we can note that 35% minimum pass marks could enable 350 candidates to pass out of 500 candidates.