Question

The length of a coil of copper wire is a random variable with mean 150 m and standard deviation 4 m. If we choose five coils of wire at random, what is the variance of the total length of the wire in the coils

Answer 1

Answer:

80 square m

Step-by-step explanation:

We are given that

Mean=150 m

S.D=4 m

We have to find the variance of the total length of the wire in the coils.

Let X1, X2,X3,X4 and X5 are random variable of sample space of coil are choosing.

Var$(X_i)=(S.D)^2=(4)^2=16$ for  all i=1 to 5

Let X be the total length of coils

$X=X_1+X_2+X_3+X_4+X_5$

$Var(X)=Var(X_1)+Var(X_2)+Var(X_3)+Var(X_4)+Var(X_5)$

$Var(X)=16+16+16+16+16=80m^2$

Hence, the variance of the total length of the wire in the coils=80 square m

Answer 2

The variance of the total length of the wire in the coils is 80 square meters

The given parameters are:

Mean = 150 meters

Standard deviation = 4 meters

The variance of one coil is calculated as:

$Variance = \sigma^2$

So, we have:

$Var= 4^2$

$Var= 16$

For five coils of wire, we have:

$Var(5) = 5 *16$

$Var(5) = 80$

Hence, the variance of the total length of the wire in the coils is 80 square meters

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