Question

There are 30 people that donated to a church. The amount each person donated has probability density function

$f(x) =\left\{\begin{matrix} \frac{1}{1250}(50-x), &if 0\leq x\leq 50 \\ 0, & otherwise \end{matrix}\right.$

Find out the probability that exactly 5 people donated between 20 and 30.

Answer 1

here probability that a random person donate between 20 and 30:

P(20<X<30)=$\int_{20}^{30}$ f(x) dx= $\int_{20}^{30}$ (1/1250)*(50-x) dx =(50x-x²/2)/1250 |³⁰₂₀ =0.20

hence from binomial distribution ;

probability that exactly 5 people donated between 20 and 30=P(X=5)=²⁰C₅(0.2)⁵(0.8)¹⁵=0.1746