Question

A private college report contains these statistics: \(70 \%\) of incoming freshmen attended public schools. \(75 \%\) of public school students who enroll as freshmen eventually graduate. \(90 \%\) of other freshmen eventually graduate. a) Is there any evidence that a freshman's chances to graduate may depend upon what kind of high school the student attended? Explain. b) What percent of freshmen eventually graduate?

Short answer

a) Yes, graduation rates differ by school type. b) 79.5% of freshmen eventually graduate.

Step-by-step solution

Understand the Problem

We are given the percentage of freshmen who attended public schools and their respective graduation rates. We need to determine if graduation rates depend on the type of school previously attended and calculate the total graduation rate.

Calculate Graduation Rate for Public School Students

We know that 70% of freshmen attended public schools, and 75% of these public school students graduate.To find the graduation rate for these students, multiply the proportion of public school students by their graduation rate:\[ 0.70 \times 0.75 = 0.525 \text{ or } 52.5\% \]

Calculate Graduation Rate for Non-Public School Students

From the data, 30% of freshmen attended non-public schools, and 90% of these students graduate.To find the graduation rate for these students, multiply the proportion of non-public school students by their graduation rate:\[ 0.30 \times 0.90 = 0.27 \text{ or } 27\% \]

Determine Overall Graduation Rate

Add the graduation rates from both public and non-public school students to find the overall graduation rate.\[ 52.5\% + 27\% = 79.5\% \]

Analyze Dependency on School Type

Compare the graduation rates: - Public school students have a 75% graduation rate. - Non-public school students have a 90% graduation rate. Since the graduation rates differ based on school type, there is evidence to suggest that a student's chances of graduating may depend on the type of high school attended.

Key concepts

Conditional Probability

Conditional probability allows us to determine the likelihood of an event given that another event has already occurred. This concept is crucial in understanding the influence of different factors on outcomes, such as a student's likelihood to graduate based on the type of high school attendance.

In this exercise, we explore whether a linkage exists between attending a public vs. a non-public school and graduating. We computed the graduation rates separately for public and non-public school students. The conditional probability, in this case, is the likelihood of graduating given the type of high school attended.

• The probability of graduating for public school students is 75%.
• The probability of graduating for non-public school students is 90%.

Analyzing these probabilities shows an apparent difference depending on the school type, suggesting that the graduation rates are not independent of the school attended.

Graduation Rate

The graduation rate represents the percentage of students who successfully complete their college program within a specified timeframe. Recognizing the graduation rate is essential for educational organizations as it reflects both student success and institutional effectiveness.

In the context of this problem, the overall graduation rate provides insight into the performance of incoming freshmen, regardless of their high school background. To calculate the overall graduation rate, we combine the probabilities of graduation for both public and non-public school attendees.

• 52.5% of freshmen from public schools graduate.
• 27% of freshmen from non-public schools graduate.
• Overall graduation rate = 52.5% + 27% = 79.5%

This combined graduation rate illustrates the general success rate of the freshman class and helps in identifying any trends or areas that might need attention.

Educational Statistics

Educational statistics is the study of numerical data related to education, providing insights into patterns, relationships, and trends affecting students and institutions. These statistics are invaluable for making informed decisions regarding education policies and practices.

In this exercise, we deal with statistics related to the high school origins of college freshmen and their corresponding graduation rates. Such statistics not only help in assessing the educational achievements but also in uncovering underlying factors that impact those achievements.

• 70% of college freshmen came from public schools, with a 75% graduation rate.
• 30% were from other schools, with a 90% graduation rate.

By analyzing these numbers, educational stakeholders can evaluate the effectiveness of pathways leading to college and address any disparities in educational outcomes. Understanding these statistics is crucial to improving educational programs and ensuring broad student success.