Answered

A sample of 334 students at a university is surveyed. The students are classified according to gender ("female" or "male"). They are also classified according to major ("biology", "business", "engineering", "mathematics", or "computer science"). The results are given in the contingency table below.

\begin{tabular}{|c|c|c|c|c|c|}
\hline & Biology & Business & Engineering & Mathematics & Computer Science \\
\hline Female & 46 & 48 & 21 & 41 & 39 \\
\hline Male & 39 & 17 & 20 & 16 & 47 \\
\hline
\end{tabular}

Among all the students in the sample, what is the relative frequency of male computer science majors? Round your answer to two decimal places.

[tex]\(\square\)[/tex]



Answer :

GinnyAnswer
Sure, let's break down the problem into simpler steps to understand how we arrive at the relative frequency of male computer science majors.

1. Identify the total number of students surveyed:
The problem states that a sample of 334 students at a university is surveyed.

2. Identify the number of male computer science majors:
According to the contingency table, there are 47 male computer science majors.

3. Calculate the relative frequency:
The relative frequency is found by dividing the number of male computer science majors by the total number of students surveyed.
[tex]\[ \text{Relative frequency} = \frac{\text{Number of male computer science majors}}{\text{Total number of students}} = \frac{47}{334} \][/tex]

4. Simplify the fraction and calculate the value:
After performing the division, we get:
[tex]\[ \frac{47}{334} \approx 0.1407185628742515 \][/tex]

5. Round the result to two decimal places:
To provide a more concise answer, we'll round the relative frequency to two decimal places.
[tex]\[ 0.1407185628742515 \approx 0.14 \][/tex]

Therefore, the relative frequency of male computer science majors among all the students in the sample is [tex]\(0.14\)[/tex].