represent the times necessary to perform three successive repair tasks at a service facility. Suppose they are normal random variables with means of 50 minutes, 60 minutes, and 40 minutes, respectively. The standard deviations are 15 minutes, 20 minutes, and 10 minutes, respectively

Question: The question is incomplete. What need to be calculated is not included in the question. Below is the question requirement and the answer.

a) Suppose X1, X2, and X3 are independent. All three repairs must be completed on a given object. What is the mean and variance of the total repair time for this object?

Answer:

Mean = 50 minutes

Variance = 725 minutes

Step-by-step explanation:

X₁ = 50

X₂ = 60

X₃ = 40

σ₁ = 15

σ₂ = 20

σ₃ = 10

Calculating the mean E (Y) using the formula;

E (Y) = E (X₁ + X₂ + X₃) / 3

= (EX₁ + EX₂ + EX₃) / 3

= (50 + 60 + 40) / 3

= 50 minutes

Therefore, the mean of the total repair time for this object is 50 minutes

Calculating the variance V (Y) using the formula;

V (Y) = V (X₁ + X₂ + X₃)

= E (X₁) + E (X₂) + E (X₃)

= σ₁² + σ₂² + σ₃²

= 15² + 20² + 10²

= 225 + 400 + 100

= 725 minutes

Therefore, the variance of the total repair time for this object is 725 minutes