Question

The following incomplete contingency table shows a random sample of 200 cyclists and the routes they prefer. Lake Path Hilly Path Wooded Path Total Female 45 110 Male 52 12 Total 71 90 Determine the total number of cyclists who prefer a Wooded Path. Do not type the units in your answer.

Answer 1

To find the total number of cyclists who prefer a Wooded Path, we need to complete the contingency table by filling in the missing values.

Lake Path | Hilly Path | Wooded Path | Total
:--: | :--: | :--: | :--:
Female | 45 | | | 155
Male | 52 | 12 | | 64
Total | 97 | 90 | | 219

We know that the total sample size is 200, so we can fill in the missing value in the Wooded Path column by subtracting the sum of the other two columns from 200:

Lake Path | Hilly Path | Wooded Path | Total
:--: | :--: | :--: | :--:
Female | 45 | | 110 | 155
Male | 52 | 12 | 36 | 64
Total | 97 | 90 | 146 | 219

Therefore, the total number of cyclists who prefer a Wooded Path is 146.

Answer 2

To determine the total number of cyclists who prefer a Wooded Path, we can complete the contingency table and calculate the sum for the Wooded Path category.

The given incomplete contingency table is:

We need to fill in the missing values in the contingency table.

To find the total number of cyclists who prefer a Wooded Path, we need to calculate the sum for the Wooded Path category.

The sum for the Wooded Path category can be obtained by subtracting the sum of the other two paths (Lake Path and Hilly Path) from the total count of cyclists:

`\sf\:\text{Wooded Path} = \text{Total} - (\text{Lake Path} + \text{Hilly Path})\\`

Substituting the given values:

`\sf\:\text{Wooded Path} = 200 - (71 + 90)\\`

Calculating:

`\sf\:\text{Wooded Path} = 200 - 161\\`

`\sf\:\text{Wooded Path} = 39 \\`

Therefore, the total number of cyclists who prefer a Wooded Path is 39.

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