Problem 29 - 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(math or statistics)

Step-by-Step Solution

Answer

The probability is approximately 0.007.

Step 1: Calculate the Total Number of Students

Sum all the students from each category in the table to find the total number of students who took the MCAT. \[\text{Total students} = 15819 + 963 + 179 + 2770 + 2482 + 1431 + 1761 = 25,405\]

Step 2: Identify the Number of Students in Math or Statistics

Identify the number of students who majored in math or statistics from the table, which is given as 179.

Step 3: Calculate the Probability

Calculate the probability by dividing the number of math or statistics students by the total number of students. Express this probability as a decimal.\[P(\text{math or statistics}) = \frac{179}{25,405}\approx 0.007\]

Step 4: Rounding

Round the probability to the nearest thousandth. Since 0.007 is already rounded to the thousandth place, no further rounding is needed.

Key Concepts

MCAT statistics

The Medical College Admission Test, commonly known as the MCAT, is a critical exam for prospective medical students in the United States. It covers a wide range of subjects to ensure that students have a well-rounded knowledge base before entering medical school. For those curious about the statistical aspects, it's interesting to analyze the backgrounds of test-takers.
This involves looking at the college majors of the students, which can reveal trends in who takes the MCAT and from what fields they come. This data helps both educators and students better understand patterns that may influence admission strategies or study focus. Each major is represented by a specific number of students, which can be analyzed through various statistical methods.

college majors

Considering the diverse backgrounds of students taking the MCAT, their college majors provide a wealth of information. Let's take a closer look at the majors listed for the MCAT takers:

• Biological sciences
• Humanities
• Math or statistics
• Physical sciences
• Social sciences
• Specialized health sciences
• Other

Each major group brings unique skills and perspectives to the medical field. For instance, biological sciences may appear to be a natural choice for many, being directly related to medicine. However, majors like humanities and social sciences offer valuable insights into human behavior and ethics. Recognizing these distinctions is crucial for comprehending how diverse educational backgrounds enrich the medical profession.

probability calculation

Probability is a fundamental concept in statistics that quantifies the likelihood of an event happening. In the context of the MCAT exercise, we're interested in the probability of choosing a student who majored in math or statistics.
Firstly, we need the total number of students from all listed majors. We add up the number of students for each category to get this total, which is 25,405.
Next, calculate the probability by dividing the number of students who majored in math or statistics by this total. Therefore, the probability is given by: \[P(\text{math or statistics}) = \frac{179}{25,405}\approx 0.007\] This means there is approximately a 0.7% chance of randomly selecting a student from this major group.

decimal rounding

Rounding decimals is an essential skill in statistics, ensuring clarity and simplicity when reporting probabilities. The concept involves reducing the number of decimal places to make the number easier to understand, often to the nearest thousandth.
In this exercise, we calculated a probability to be approximately 0.007. Because this number is already in the thousandth place, no further rounding is necessary.
However, understanding when and how to round is crucial. When the digit immediately after your desired rounding place is 5 or more, you round up. If it's less, you round down. Practicing these guidelines helps in consistently reporting probabilities accurately and clearly.