Woodworkers Alex and Brandon make precision pieces for various toys. One of the

Question

Woodworkers Alex and Brandon make precision pieces for various toys. One of the toys they make requires four 8-inch long sticks. When Alex makes 8-inch long sticks, he cuts them one at a time and tosses them into a storage bin. Alex’s sticks have a mean length of 8.10 inches and a standard deviation of 0.15 inches. Brandon uses a different approach. He wants his four 8-inch sticks to be identical, so he makes them by clamping together 4 boards and then cutting them all at once. After each cut, Brandon measures the sticks while they are still clamped together (and all 4 are given the same measurement). His cuts have a mean length of 8.05 inches and a standard deviation of 0.1 inches.

a.   Suppose we take 1 of Alex’s sticks, 2 of Brandon’s sticks (both from the same cut), lay them end to end, and measure the combined length.

The mean length will be ___________________.

The standard deviation of the length will be __________________.

b.   Suppose we take 1 of Alex’s sticks, 2 of Brandon’s sticks (from different cuts), lay them end to end, and measure the combined length.

The mean length will be ___________________.

The standard deviation of the length will be __________________.

Explanation / Answer

a)

i)

The mean length will be 8.1

The standard deviation of the length will be 0.15

b.   Suppose we take 1 of Alex’s sticks, 2 of Brandon’s sticks (from different cuts), lay them end to end, and measure the combined length.

The mean length will be 8.05

The standard deviation of the length will be 0.1

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