Problem 31 - Algebra 2

Question

Use the table that shows the college majors of the students who took the Medical College Admission Test (MCAT) recently. $$\begin{array}{|l|l|}\hline \text { biological sciences } & {15,819} \\\ \hline \text { humanities } & {963} \\ \hline \text { math or statistics } & {179} \\ \hline \text { physical sciences } & {2770} \\ \hline \text { social sciences } & {2482} \\ \hline \text { specialized health sciences } & {1431} \\ \hline \text { other } & {1761} \\ \hline\end{array}$$ If a student taking the test were randomly selected, find each probability. Express as decimals rounded to the nearest thousandth. P(physical sciences)

Step-by-Step Solution

Answer

The probability is approximately 0.109.

Step 1: Identify the Total Number of Students

To find the probability, we need the total number of students who took the test. Add up all the students from each category to get the total number of students.\[ 15,819 + 963 + 179 + 2770 + 2482 + 1431 + 1761 = 25,405 \]

Step 2: Identify the Number of Students in the Desired Category

Identify the number of students who majored in physical sciences from the table. There are 2770 students in this category.

Step 3: Calculate the Probability

To calculate the probability of selecting a student in physical sciences, divide the number of physical sciences students by the total number of students.\[ P(\text{physical sciences}) = \frac{2770}{25405} \]

Step 4: Simplify and Round the Probability

Perform the division and round the result to the nearest thousandth.\[ \frac{2770}{25405} \approx 0.109 \]

Key Concepts

College Majors

College majors refer to the specific fields of study that students choose when pursuing higher education. Majors are essential in shaping the academic path and career opportunities for students. When preparing for tests like the MCAT, choosing a college major can influence the foundational knowledge students bring to the exam.
In the exercise provided, students with different majors like biological sciences, humanities, and physical sciences took the MCAT. Each major represents a different area of expertise and interest for the students:

• Biological Sciences: Often preferred by those interested in medicine or life sciences.
• Humanities: Favored by students who focus on literature, history, and the arts.
• Math or Statistics: Chosen by students who enjoy dealing with numbers and data.

Understanding different college majors helps us grasp the diversity of backgrounds students bring to real-world scenarios like the MCAT.

Decimal Representation

Decimal representation is a way of expressing numbers using a base of 10. It is the most common number system used in everyday life. When dealing with probabilities, it is crucial to express them in decimal form for ease of understanding and comparison.
In the example exercise, the probability of selecting a student who majored in physical sciences was calculated as a decimal. This involves dividing the number of successful outcomes (students in physical sciences) by the total number of possible outcomes (all students who took the test).
Understanding decimal representation helps make numerical data more accessible and easier to work with, especially when performing mathematical calculations or statistical evaluations.

Rounding Numbers

Rounding numbers is a fundamental mathematical skill that involves making a number simpler while keeping its value close to what it was. In calculations involving probabilities, rounding helps us represent results in a more concise and human-readable form.
The probability found in the exercise was rounded to the nearest thousandth. Here's how you do it:

• Identify the place value: The thousandth place is the third digit to the right of the decimal point.
• Look at the digit to the right: If it's 5 or greater, round up. Otherwise, leave the rounding digit unchanged.

In the given solution, the probability \( \frac{2770}{25405} \) was approximately 0.109 after rounding. Learning how to round numbers accurately is essential for working with estimates and presenting results clearly.

MCAT

The Medical College Admission Test (MCAT) is a critical standardized examination for aspiring medical students. It assesses potential entrants on various skills needed for a successful medical career, like critical thinking, problem-solving, and knowledge of natural, behavioral, and social science concepts.
Each year, students from diverse majors take the MCAT, reflecting the interdisciplinary nature of medical studies. While many test-takers come from biological sciences, students from less traditional pre-med backgrounds, such as humanities or physical sciences, also apply their unique skills to the exam.
Understanding the significance and scope of the MCAT helps students from any major prepare effectively and showcases the broad range of backgrounds that contribute to the medical field.