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: m₁ = 28.1 minutes; s₁ = 8.2 minutes

Repair computer, x₂: m₂ = 90.5 minutes; s₂ = 15.2 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.

(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.

(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.