Math  /  Data & Statistics

QuestionThe following table shows the results of a survey of 100 authors by a publishing company. \begin{tabular}{|r|c|c|c|} \hline & New Authors & Established Authors & Total \\ \hline Successful & 4 & 26 & 30 \\ \hline Unsuccessful & 16 & 54 & 70 \\ \hline Total & 20 & 80 & 100 \\ \hline \end{tabular}
Compute the relative frequency of the given event if an author as specified is chosen at random. A successful author is established. .26.26

Studdy Solution

STEP 1

What is this asking? Out of all the authors, what's the chance we pick a successful *and* established one? Watch out! Don't mix up "successful author" with "successful *established* author".
There are way more established authors than new ones, so pay attention to that!

STEP 2

1. Find the total number of authors.
2. Find the number of successful and established authors.
3. Calculate the relative frequency.

STEP 3

The problem says there are a total of **100** authors surveyed.
Easy peasy!
We'll need this number later.

STEP 4

The table tells us there are **26** authors who are both successful *and* established.
Boom!

STEP 5

Remember, *relative frequency* just means the chance of something happening out of the total possibilities.
It's like asking, "Out of all the authors, what fraction are successful *and* established?".

STEP 6

We know there are **26** successful and established authors, and **100** total authors.
So, the relative frequency is just the number of successful and established authors divided by the total number of authors.

STEP 7

Let's do the math! 26100=0.26 \frac{\textbf{26}}{\textbf{100}} = \textbf{0.26}

STEP 8

The relative frequency of choosing a successful established author is **0.26**.

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