Question

50 students live in a dormitory. The parking lot has the capacity for 30 cars. If each student has a car with probability 1 2 (independently from other students), what is the probability that there won’t be enough parking spaces for all the cars.

Answer 1

This is a binomial distribution wit n=50, p=0.5.

Normal approximation of this distribution has

$\mu=np=50*0.5=25,\;\sigma=\sqrt{np(1-p)}=\sqrt{50*0.5*0.5}=3.5355.$

$P(X>30)=P(Z>\frac{30-25}{3.5355})=P(Z>1.41)=1-P(Z<1.41)=0.0793.$