# Two owners of a cattle ranch, Jo and Val, want to find the average weight for the ranch’s 200 cows. Instead of weighing all of the cows: Jo weighs 25 cows and gets an average weight of 1,350 pounds (stdev 50) Val weighs 100 cows and gets an average weight of 1,420 pounds (stdev 50) What is Jo’s margin of error, rounded to the nearest whole number?

Question
Confidence intervals
Two owners of a cattle ranch, Jo and Val, want to find the average weight for the ranch’s 200 cows. Instead of weighing all of the cows:
Jo weighs 25 cows and gets an average weight of 1,350 pounds (stdev 50)
Val weighs 100 cows and gets an average weight of 1,420 pounds (stdev 50)
What is Jo’s margin of error, rounded to the nearest whole number?

2020-10-29
Step 1
Margin of Error can be calculated by:
$$\displaystyle{M}={z}\times\frac{\sigma}{\sqrt{{n}}}$$
where: z depends on the confidence interval with we are working,
Let's assume $$95\%$$ as the confidence interval,
So, $$\displaystyle{z}={1.96}$$
Step 2
Here :
Standard deviation $$\displaystyle{\left(\sigma\right)}={50}$$
N is the no. of sample,
Hence,
We have:
$$\displaystyle{M}={1.96}\times\frac{50}{\sqrt{{25}}}$$
$$\displaystyle={1.96}\times{10}$$
$$\displaystyle={19.6}$$
Rounding to the nearest whole number we get:
$$\displaystyle{M}={20}$$
Hence,
Jo's margin of error is 20(rounded to the nearest whole number).

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