Woodworkers Alex and Brandon make precision pieces for toys. Each toy requires four 8-inch long sticks. Alex cuts four sticks one at time, and their lengths are independent. Alex’s sticks have mean length 8 inches with a standard deviation 0.15 inches. Brandon clamps four sticks together and cuts them all at once, so that they all have the same length. Brandon’s sticks also have a mean length of 8 inches with a standard deviation of 0.15 inches.
a. Alex’s four sticks are laid end-to-end. What is the mean of the total length? What is the standard deviation of the total length?
b. Brandon’s four sticks are laid end-to-end. What is the mean of the total length? What is the standard deviation of the total length?
c. Four sticks, two from Alex and two from Brandon, are laid end-to-end. What is the mean of the total length? What is the standard deviation of the total length?
Let denote the lengths of Alex’s sticks. Then
are independent with mean 8 and standard deviation 15. Let Y denote the length of Brandon’s sticks. Then Y has mean 8 and standard deviation 0.15. Let A denote the total length of Alex’s sticks, let ? denote the total length of Brandon’s sticks, and let C denote the length of two sticks from Alex plus two sticks from Brandon.
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