The probability distribution of a random variable $X$ is given below. If $E(X)=\dfrac{263}{15}$, then $P(X<20)$ is equal to:
Step-by-Step Solution
Key Concept: $E(X)=\sum X_i P(X_i)=\tfrac{526k}{15\times7}=\tfrac{263}{15}\Rightarrow k=\tfrac{7}{2}$. Values of $X$: 14, 15, 16, 17, 18, 19, 20, 21.
$k=\tfrac{7}{2}$. $P(X<20)=\tfrac{11}{15}$.
Correct Answer: 1