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 x_{1} and x_{2} be random variables representing the lengths of time in minutes to examine a computer (x_{1}) and to repair a computer (x_{2}). Assume x_{1} and x_{2} are independent random variables. Long-term history has shown the following times.
Examine computer, x_{1}: μ_{1}
= 29.7 minutes; σ_{1} = 8.0 minutes
Repair computer, x_{2}: μ_{2} =
91.0 minutes; σ_{2} = 14.2 minutes
(a) Let W = x_{1} + x_{2} 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 | |
σ^{2} | |
σ |
(b) Suppose it costs $1.50 per minute to examine the computer and
$2.75 per minute to repair the computer. Then W =
1.50x_{1} + 2.75x_{2} 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 | |
σ^{2} | |
σ |
(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 =
1.5x_{1} + 50. Compute the mean, variance, and
standard deviation of L. (Round your answers to two
decimal places.)
μ | |
σ^{2} | |
σ |
A computer repair shop has two work centers. The first center examines the computer to see...
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 and be random variables representing the lengths of time in minutes to examine a computer () and to repair a computer (). Assume and are independent random variables. Long-term history has shown the following mean and standard deviation for the two work centers: Examine computer, : = 27.3 minutes; = 7.5 minutes Repair...
A computer reputophawo work centers. The first center examines the computer to what is wrong, and the second center reals the computer and a ndo variables representing the lengths of time in minutes to examine a computer and to repair a computer (*). Assumex, and are independent random variables, Long term History has shown the following times. Examine computer, X, Mi27.9 minutes: 0,74 minutes Repair computer, Xy: 12 = 92.0 minutes: 0 - 15.3 minutes (a) Let w Xybe a...
Insurance companies know the risk of insurance is greatly reduced if the company insures not just one person, but many people. How does this work? Let x be a random variable representing the expectation of life in years for a 25-year-old male (i.e., number of years until death). Then the mean and standard deviation of x are μ = 49.3 years and σ = 11.1 years (Vital Statistics Section of the Statistical Abstract of the United States, 116th Edition). Suppose...
Insurance companies know the risk of insurance is greatly reduced if the company insures not just one person, but many people. How does this work? Let x be a random variable representing the expectation of life in years for a 25-year-old male (i.e., number of years until death). Then the mean and standard deviation of x are μ = 49.0 years and σ = 10.3 years (Vital Statistics Section of the Statistical Abstract of the United States, 116th Edition). Suppose...
Q410 pts].An appliance manufacturer wants to contract with a repair shop to ed repairs in Indianapolis. The of repair time of 55 minutes to 95 minutes. Two firms have submitted bids for the work. In test trials, one firm had a mean repair time of 73 minutes with a standard deviation of 4.2 minutes and the other firm had a mean repair time of 72 minutes with a standard deviation of 5.7 minutes. Which firm would you choose and why?...
An appliance manufacturer wants to contract with a repair shop to handle authorized repairs in Indianapolis. The company has set an acceptable range of repair time of 47.00 minutes to 91.00 minutes. Two firms have submitted bids for the work. In test trials, Firm A had a mean repair time of 65.00 minutes with a standard deviation of 4.00 minutes; and the other firm, Firm B, had a mean repair time of 67.00 minutes with a standard deviation of 4.50...
Problem 5 of 5Sum of random variables Let Mr(μ, σ2) denote the Gaussian (or normal) pdf with Inean ,, and variance σ2, namely, fx (x) = exp ( 2-2 . Let X and Y be two i.i.d. random variables distributed as Gaussian with mean 0 and variance 1. Show that Z-XY is again a Gaussian random variable but with mean 0 and variance 2. Show your full proof with integrals. 2. From above, can you derive what will be the...
There are two traffic lights on a commuter's route to and from work. Let X1 be the number of lights at which the commuter must stop on his way to work, and X2 be the number of lights at which he must stop when returning frorm work. Suppose that these two variables are independent, each with the pmf given in the accompanying table (so X1, X2 is a random sample of size n = 2). μ-09, σ. 0.69 p(%) 0.4...
Let X1, X2, ..., X9 be a sample of Normal random variables with expectation μ=72 and variance σ2=49. (Namely, standard deviation of σ=7.) Consider the statistic T = (X-72)/[S/ √9], where X is the sample average and S2 is the sample variance. The probability P(T ≤ 2) is best described by: Select one: a. 0.95 b. 0.96 c. 0.97 d. 0.98
The owner of a computer repair shop has determined that their daily revenue has mean $7200 and standard deviation $1200. The daily revenue totals for the next 30 days will be monitored. What is the probability that the mean daily revenue for the next 30 days will be between $7000 and $7500? O 0.2661 0.8351 O 0.1649 O 0.7339