Question

A used car dealer gets complaints about his cars: as shown: Number of complaints per day: 0 complaints per day =probability 0.01; 1 complaint per day = probability 0.04, 3 complaints per day = probability 0.21; 4 complaints per day = probability 0.44; 5 complaints per day= 0.11 probability; 6 complaints per day = 0.09 probability. Find the expected number of complaints per day.

Answer 1

The formula for the expected number of complaints is as follows:

$E(x)=x_1\lbrack P(x_1)\rbrack+x_1\lbrack P(x_2)\rbrack+\cdots+x_n\lbrack P(x_n)\rbrack$

Substitute the given values into the equation.

$E(x)=0(0.01)+1(0.04)+2(0.1)+3(0.21)+4(0.44)+5(0.11)+6(0.09)$

Simplify the right side of the equation. Multiply and then find the sum of the products.

$\begin{gathered} E(x)=0+0.04+0.2+0.63+1.76+0.55+0.54 \\ =3.72 \end{gathered}$

Thus, there are approximately 3.72 or 4 complaints in a day.