Question from glassdoor:
Chance that a student passes the test is 10%. What is the chance that out of 400 students AT LEAST 50 pass the test? Check the closest answer: The offered answers were 5%, 10%, 15%, 20%, 25%.
Let $X_i=1$ if $i'$th student passes the test and $X_i=0$ if fails. Also, let $X=\sum_{i=1}^{400}X_i$. Then $X$ form a binomial distribution with $p=0.1$ and $n=400$. Thus,
$\Pr(X\geq50)=1-\Pr(X\leq49)=1-\sum_{x=0}^{49}\binom{400}{x}0.1^x0.9^{400-x}.$
But I don't know if there is any easy way to approximate the above value.
Also, maybe one way is to use mean and variance: $E[X]=np=40$ and $\mathrm{var}(X)=np(1-p)=36$?
This was an interview question so I imagine no calculating device was allowed. It can be done without external aid if you have a background in elementary Statistics.
We have to estimate $P(X\ge 50)$ where $X$ is binomial with $n=400$ and $p=0.1$.
Using the normal approximation to the Binomial distribution and a continuity correction, as suggested in the comments. we have to find $P(Y\ge 49.5)$ where $Y$ is normal with mean $40$ and variance $36$.
This is $P(Z> \frac{49.5-40}{6}) = P(Z>1.6)$ where $Z$ is the standard normal distribution.
This probability is approximately $5\%$. (The actual value giving $5\%$ is around $1.65$ which any statistician should know).