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?

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

step-by-step explanation:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

step-by-step explanation:

given that megan owns a clothing boutique.

the profits of 2010, 11, are recorded and shown as follows:

years since     2010 0     1     2     3       4       5

profits made in 1000's   39       84     111     120   111     84

we find that profit gradually increases form 2010 to 2013 upto 120,   then starts decreasing.

the profits for 2012 and 2014 are the same while that of 2011 and 2015 are also the same.

this shows that there is symmetry about the line profit = 120000

hence answer is:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

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3< x< 5

step-by-step explanation:

|x - 4| < 1

there are two solutions, one positive and one negative.   remember to flip the inequality when taking the negative solution

x-4 < 1       x-4 > -1

add 4 to each side

x-4+4 < 1+4       x-4+4 > -1+4

x< 5                 x> 3

3< x< 5