Two owners of a cattle ranch, Robert and

LaDon Fox

LaDon Fox

Answered question

2022-07-21

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 & Explanation

xleb123

xleb123

Skilled2023-06-03Added 181 answers

To find Val's margin of error for the average weight of the ranch's cows, we can use the formula:
Margin of Error=1.96×(Standard DeviationN)
Given information:
Standard Deviation (stdev) = 50
Number of cows weighed by Val (N) = 100
Substituting these values into the formula, we have:
Margin of Error=1.96×(50100)
Simplifying the expression inside the parentheses:
Margin of Error=1.96×(5010)
Simplifying further:
Margin of Error=1.96×5
Calculating the product:
Margin of Error=9.8
Rounding the margin of error to the nearest whole number, we get:
Margin of Error10
Therefore, Val's margin of error for the average weight of the ranch's cows is approximately 10 pounds.

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