Question

Lifetime of a certain transistor in a certain application has a mean of 900 hours and a standard deviation of 30 hours. Four transistors are used, and the total length of time that the four resistors last is recorded. The transistors are independent of one another. What is the mean length of time in hours that the four transistors will last?

Answer 1

3600 hours

Explanation:

let total life time of t four transistors T = X1 + X2 + X3 + X4 (where X1,X2,X3 and X4 are life time of individual transistors

mean of the length of time that four transistors will last =E(T)=E(X1 + X2 + X3 + X4)

=E(x1) + E(x2) + E(x3) + E(x4) =900+900+900+900 =3600

and standard deviation of total time =SD(T)=sqrt(Var(T)) = sqrt(Var(X1) + Var(x2) + Var(x3) + Var(x4))

where sqrt means the square root

=sqrt(302+302+302+302) =sqrt(3600) =60