Estimation usually means you want an answer good to one or maybe two significant figures. That usually means you want to round the numbers involved to one or two significant figures.

Doing that here transforms the problem to 180/3 = 60, an answer with one significant figure.

You can improve the estimate a bit by recognizing that it is a little high (the numerator is higher than 175.32, but the denominator is the same). Since the numerator is high by about 5, the estimate is high by about 5/3 or a little less than 2. A closer estimate will be 60 - 2 = 58.

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The degree to which you refine the estimate will depend on the error requirements you have. Certainly an estimate of 60 is within 10% of the true value, so is "close enough" for many purposes.

7 0

3 years ago

4. The following intervals were plausible population proportions for a given sample. Find the margin of error in each case.

Vedmedyk [2.9K]

Answer: a. 0.15 b. 0.03 c. 0.055 d. 0.05

Step-by-step explanation:

For plausible intervals of population proportions , the margin of error is basically half of the difference between upper limit and lower limit.

a. Interval = From 0.35 to 0.65

Upper limit = 0.65

Lower limit = 0.35

Difference = Upper limit- Lower limit

= 0.65-0.35=0.30

Margin of error = (Difference)÷2 =(0.30)÷2=0.15

b. Interval = From 0.72 to 0.78

Upper limit = 0.78

Lower limit = 0.72

Difference = 0.78-0.72 = 0.06

Margin of error =(0.06)÷2=0.03

c. Interval = From 0.84 to 0.95

Upper limit = 0.95

Lower limit = 0.84

Difference =0.95-0.84= 0.11

Margin of error = (0.11)÷2 = 0.055

d.Interval = From 0.47 to 0.57

Upper limit = 0.57

Lower limit = 0.47

Difference = 0.57-0.47=0.10

Margin of error = (0.10)÷2=0.05

3 0

3 years ago