Math

Question Estimate the proportion of oil tankers that had spills given a sample of 712 tankers, where 570 did not have spills. Enter the result as a fraction or decimal rounded to 3 decimal places.

Studdy Solution

STEP 1

Assumptions
1. A sample of 712 tankers is considered.
2. Out of these, 570 tankers did not have spills.
3. We want to estimate the proportion of tankers that had spills.

STEP 2

First, we need to find the number of tankers that had spills. We can do this by subtracting the number of tankers without spills from the total number of tankers.
Numberoftankerswithspills=TotalnumberoftankersNumberoftankerswithoutspillsNumber\, of\, tankers\, with\, spills = Total\, number\, of\, tankers - Number\, of\, tankers\, without\, spills

STEP 3

Now, plug in the given values to calculate the number of tankers that had spills.
Numberoftankerswithspills=712570Number\, of\, tankers\, with\, spills = 712 - 570

STEP 4

Calculate the number of tankers that had spills.
Numberoftankerswithspills=712570=142Number\, of\, tankers\, with\, spills = 712 - 570 = 142

STEP 5

Next, we need to find the proportion of tankers that had spills. We can do this by dividing the number of tankers with spills by the total number of tankers.
Proportionoftankerswithspills=NumberoftankerswithspillsTotalnumberoftankersProportion\, of\, tankers\, with\, spills = \frac{Number\, of\, tankers\, with\, spills}{Total\, number\, of\, tankers}

STEP 6

Plug in the values to calculate the proportion of tankers that had spills.
Proportionoftankerswithspills=142712Proportion\, of\, tankers\, with\, spills = \frac{142}{712}

STEP 7

Calculate the proportion of tankers that had spills.
Proportionoftankerswithspills=1427120.199Proportion\, of\, tankers\, with\, spills = \frac{142}{712} \approx 0.199

STEP 8

Round the proportion to three decimal places as instructed.
Proportionoftankerswithspills0.199Proportion\, of\, tankers\, with\, spills \approx 0.199
The estimated proportion of oil tankers that had spills is approximately 0.199, or as a fraction 142712\frac{142}{712}.

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