Question

A coordinator of a degree program in a university assessed a probability distribution for the number of students (x) entering into the program as follows:

X 30 45 60 65 90 100

f(x) 0.10 0.20 0.20 0.30 0.10 0.10

(i) Is the probability distribution valid? Explain

(ii) What is the probability of 60 or fewer students entering into the program?  

Answer 1

In order to verify that the distribution is valid, we need to check that: $\sum_xf(x)=1$. We receive: $0.1+0.2+0.2+0.3+0.1+0.1=1$.

(ii) Denote by $X$ a random variable that corresponds to that distribution. We need to calculate $P(X\leq60)$. We receive: $P(X\leq60)=P(X=30)+P(X=45)+P(X=60)=0.1+0.2+0.2=0.5$

Thus, the probability is $0.5.$