Question

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? (The formula is


10


20


50


529

Answer 1

Answer:

Required margin of error  = 20

Step-by-step explanation:

Required margin of error = 20

so , option (2) is the correct answer.

Explanation:

Values are given as,

we will have to need confidence level to calculate margin of error so ,we assume 95% confidence level .



z = 1.96 (critical value of 95%)

sample size n = 25

standard deviation = 50

Using the formula

Margin of error E =  z∗(σ/ n )  

putting the values

1.96∗(50/ 25)  

= 19.6

=20

Required margin of error :  E = 20

Answer 2

Answer: Jo's margin of error is M = 20

Step-by-step explanation:

The margin of error can be calculated as:

M = z*σ/√n

where:

z depends on the confidence interval with we are working, let's use 95%, so z = 1.96

σ = standard deviation = 50

n = number of the sample.

So for Jo we have:

M = 1.96*50/√25 = 1.96*50/5 = 1.96*10 = 19.6

So if we round it to the nearest whole number, we should round up, and we get:

M = 20