Question

A computer repair shop has two work centers. The first center examines the computer to see what is wrong, and the second center repairs the computer. Let x1 and x2 be random variables representing the lengths of time in minutes to examine a computer (x1) and to repair a computer (x2). Assume x1 and x2 are independent random variables. Long-term history has shown the following times. Examine computer, x1: μ1 = 31.0 minutes; σ1 = 8.8 minutes Repair computer, x2: μ2 = 87.0 minutes; σ2 = 14.8 minutes (a) Let W = x1 + x2 be a random variable representing the total time to examine and repair the computer. Compute the mean, variance, and standard deviation of W. (Round your answers to two decimal places.)

μ 118 Correct: Your answer is correct. σ2 296.44 Incorrect: Your answer is incorrect. σ 17.21 Incorrect: Your answer is incorrect. (b) Suppose it costs $1.50 per minute to examine the computer and $2.75 per minute to repair the computer. Then W = 1.50x1 + 2.75x2 is a random variable representing the service charges (without parts). Compute the mean, variance, and standard deviation of W. (Round your answers to two decimal places.) μ 285.75 Correct: Your answer is correct. σ2 (No Response) σ 26.805 Incorrect: Your answer is incorrect. (c) The shop charges a flat rate of $1.50 per minute to examine the computer, and if no repairs are ordered, there is also an additional $50 service charge. Let L = 1.5x1 + 50. Compute the mean, variance, and standard deviation of L. (Round your answers to two decimal places.) μ 96.5 Correct: Your answer is correct. σ2 174.24 Correct: Your answer is correct. σ 13.2 Correct: Your answer is correct.

Answer 1

a)

W = x1+ x2

mean = E(X1) +E(X2) = 31 + 87

= 118

variance (X1+X2)= Var(X1) + Var(X2)

= 8.8^2 + 14.8^2

= 296.48

sd = sqrt(Variance)

=sqrt(296.48)

= 17.21859

=17.22

b)

W = 1.5 x1 + 2.75 x2

E(W) = 1.5 * 31 + 2.75 * 87 = 285.75

Var(W) = 1.5^2 * 8.8^2 + 2.75^2 * 14.8^2 = 1830.73

sd = sqrt( 1830.73 ) = 42.79

c)

L = 50 + 1.5 x1

E(L) = 50 +1.5 * 31 = 96.5

Var(L) = 1.5^2 * 8.8^2 = 174.24

sd(L) = sqrt( 174.24 ) = 13.2

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