A factory has a machine that makes steel rods. The length of rids that the machine makes follows a normal distribution curve with a mean of 11.5 feet and a standard deviation of 0.3 feet. The factory manager does not want to use the rods from the bottom 20% and the top 15%. Find the rod length the manager will be using as the basis for separating the rods.

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mattiano01 mattiano01

21-01-2019
Mathematics

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A factory has a machine that makes steel rods. The length of rids that the machine makes follows a normal distribution curve with a mean of 11.5 feet and a standard deviation of 0.3 feet. The factory manager does not want to use the rods from the bottom 20% and the top 15%. Find the rod length the manager will be using as the basis for separating the rods.

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ejhuff ejhuff · Answer 1 · 2019-01-21T12:45:50+01:00

Answer:

The manager will specify that rods shorter than 11 feet 2.97 inches (or perhaps 11 ft 2 and 7/8 in, but probably not 11 ft 3.0 in), or longer than 11 ft 9.731 in, (or 11 ft 9 and 5/8 in but not 11 ft 9 and 3/4 in) rejected.

Step-by-step explanation:

You need to know some way or other of getting values of the cumulative normal distribution. I used the query "20th percentile of normal distribution μ=11.5 σ=0.3" at wolfram alpha. You can write "mean 11.5 standard deviation 0.3" instead of "μ=11.5 σ=0.3"

Also ask google to "convert 11.2475 feet to inches", giving "11 feet 2.97 inches" and convert 11.8109 giving

"11 feet 9.731 inches".

The manager will specify that rods shorter than 11 feet 2.97 inches (or perhaps 11 ft 2 and 7/8 in, but probably not 11 ft 3.0 in), or longer than 11 ft 9.731 in, (or 11 ft 9 and 5/8 in but not 11 ft 9 and 3/4 in) rejected.