Question

question 8 let x be the number of students who attend an office hours session a day prior to an exam. x is known to be distributed as follows: p(x)=kx 0≤x≤5 what is the value of x being less than 4? 0.60 0.93 0.40 0

Explanation:

Step1: Find the value of k

Since $\sum_{x = 0}^{5}p(x)=1$ and $p(x)=kx$ for $0\leq x\leq5$, we have $\sum_{x = 0}^{5}kx=k\sum_{x = 0}^{5}x$. Using the sum - of - arithmetic - series formula $\sum_{i = 1}^{n}i=\frac{n(n + 1)}{2}$, here $\sum_{x=0}^{5}x=\frac{5\times(5 + 1)}{2}=15$. So $k\times15 = 1$, then $k=\frac{1}{15}$.

Step2: Calculate $P(X\lt4)$

$P(X\lt4)=\sum_{x = 0}^{3}p(x)=\sum_{x = 0}^{3}kx=k\sum_{x = 0}^{3}x$. Using the sum - of - arithmetic - series formula, $\sum_{x = 0}^{3}x=\frac{3\times(3 + 1)}{2}=6$. Since $k=\frac{1}{15}$, then $P(X\lt4)=\frac{1}{15}\times6=\frac{6}{15}=0.4$.

Answer:

$0.4$