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: ?1 = 30.4 minutes; ?1 = 8.5 minutes Repair computer, x2: ?2 = 89.9 minutes; ?2 = 14.9 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.) ? ?2 ? (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.) ? ?2 ? (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.) ? ?2 ?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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.
Repair computer, x2: ?2 = 89.9 minutes; ?2 = 14.9 minutes
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(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.)
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(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.)
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