Answer to Question #198904 in Statistics and Probability for Fakeha

Question

A firm report 35% of the probability that its accounts receivable from other business firms are overdue. If an accountant takes a random sample of five such accounts, then construct the probability distribution table for accounts are overdue.

Answer 1

Let $X=$ the number of accounts which are overdue: $X\sim Bin(n,p)$

Given $p=0.35, n=5.$

$$P(X=x)=\dbinom{n}{x}p^x(1-p)^{n-x}$$

$$P(X=0)=\dbinom{5}{0}0.35^0(1-0.35)^{5-0}$$

$$=0.1160290625$$

$$P(X=1)=\dbinom{5}{1}0.35^1(1-0.35)^{5-1}$$

$$=0.3123859375$$

$$P(X=2)=\dbinom{5}{2}0.35^2(1-0.35)^{5-2}$$

$$=0.336415625$$

$$P(X=3)=\dbinom{5}{3}0.35^3(1-0.35)^{5-3}$$

$$=0.181146875$$

$$P(X=4)=\dbinom{5}{4}0.35^4(1-0.35)^{5-4}$$

$$=0.0487703125$$

$$P(X=5)=\dbinom{5}{5}0.35^5(1-0.35)^{5-5}$$

$$=0.0052521875$$

$$\def\arraystretch{1.5} \begin{array}{c:c} x &p(x) \\ \hline 0 & 0.1160290625 \\ \hdashline 1 & 0.3123859375 \\ \hdashline 2 & 0.336415625 \\ \hdashline 3 & 0.181146875 \\ \hdashline 4 & 0.0487703125 \\ \hdashline 5 & 0.0052521875 \\ \end{array}$$