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Two owners of a cattle ranch, Robert and Val, want to find the average weight for the ranch’s 200 cows. Instead of weighing all of the cows: Robert weighs 25 cows and gets an average weight of 1,550 pounds (stdev = 50) Val weighs 100 cows and gets an average weight of 1,380 pounds (stdev = 50) What is Val’s margin of error, rounded to the nearest whole number? (The formula is 1.96 (std dev) / square root of N

Answer :

Using it's formula, it is found that Val's margin of error is of 9.8 pounds.

Margin of error:

The margin of error is given by the following equation:

[tex]M = 1.96\frac{s}{\sqrt{n}}[/tex]

In which:

  • s is the standard deviation.
  • n is the sample size.

In this problem:

  • The standard deviation is of 50, hence [tex]s = 50[/tex].
  • Val weighed 100 cows, hence [tex]n = 100[/tex].

Then:

[tex]M = 1.96\frac{s}{\sqrt{n}}[/tex]

[tex]M = 1.96\frac{50}{\sqrt{100}}[/tex]

[tex]M = 9.8[/tex]

Val's margin of error is of 9.8 pounds.

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