Question

Suppose the number of inches of rainfall each year in a city is normally distributed. For a random sample of years, the confidence interval (3.9,7.7) is generated. Find the margin of error Give just a number for your answer. For example, if you found that the margin of error was 2, you would enter 2.

Answer 1

Margin of error = 1.9 ≅2

Explanation:

Given the number of inches of rainfall each year in a city is normally distributed.

For a random sample of years, the confidence interval (3.9,7.7) is generated

We know that the confidence intervals of margin of error is defined by

x⁻ ± margin of error

x⁻ ± M.E

Given the confidence intervals are (3.9 ,7.7)

Equating lower limit x⁻ -M.E = 3.9 …(i)

Equating upper limit x⁻ +M.E = 7.7 … (ii)

adding The equations (i) and (ii) and simplification , we get

2x⁻ = 11.6

Dividing by '2' on both sides , we get

x⁻ = 5.8

This is the mean of the sample x⁻ = 5.8

now substitute mean value in equation (i)

x⁻ -M.E = 3.9

5.8 - Margin of error = 3.9

Margin of error = 5.8 - 3.9

Margin of error = 1.9 ≅2

Conclusion:-

Margin of error = 1.9 ≅2

Verification:-

In given data lower imit x⁻ -M.E = 3.9

we know that x⁻ = 5.8 and margin of error =2

5.8 -1.9 =3.9

3.9=3.9