normal distribution with mean and standard deviation

Question

In an examination the number of marks allotted to each candidate is an integer. If the marks were normally distributed, and the distribution had a mean of 45 and a standard deviation of 12, find the percentage of the candidates who would pass with a pass mark of 40

Answer 1

Hint: $P(X\geq 40)=1-P(X\leq 40)=1-\Phi\left( \frac{40-\mu}{\sigma} \right)=1-\Phi\left( \frac{40-45}{12} \right)$,

where $X \sim \mathcal N(45,12^2)$

$\Phi(z)$ is the cdf of the standard normal distribution. A table for the corresponding probabilities can be found here.