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Chapter 5: Problem 18

The same issue of The Chronicle for Higher Education referenced in Exercise 5.17 also reported the following information for degrees awarded to Hispanic students by U.S. colleges in the \(2008-2009\) academic year: A total of 274,515 degrees were awarded to Hispanic students. \- 97,921 of these degrees were Associate degrees. \- 129,526 of these degrees were Bachelor's degrees. \- The remaining degrees were either graduate or professional degrees. What is the probability that a randomly selected Hispanic student who received a degree in \(2008-2009\) a. received an associate degree? b. received a graduate or professional degree? c. did not receive a bachelor's degree?

Short Answer

Expert verified
The probability that a randomly selected Hispanic student who received a degree in 2008-2009: a. received an associate degree is \(\frac{97,921}{274,515}\). b. received a graduate or professional degree is \(\frac{274,515 - (97,921 + 129,526)}{274,515}\). c. did not receive a bachelor's degree is \(\frac{274,515 - 129,526}{274,515}\).

Step by step solution

01

Determine the total number of degrees

The total number of degrees awarded to Hispanic students in the 2008-2009 academic year is 274,515.
02

Calculation for part (a)

Part (a) is asking for the probability that a randomly selected Hispanic student received an associate degree. This can be found by dividing the number of associate degrees awarded (97,921) by the total number of degrees awarded (274,515). Using this, the calculation becomes \(P(Associate Degree) = \frac{97,921}{274,515}\).
03

Calculation for part (b)

For part (b), the question asks for the probability that a randomly selected Hispanic student received a graduate or professional degree. This is found by subtracting the number of associate and bachelor's degrees from the total number of degrees, since the question states that the remaining degrees were either graduate or professional. The calculation becomes \(P(Graduate or Professional Degree) = \frac{274,515 - (97,921 + 129,526)}{274,515}\).
04

Calculation for part (c)

Finally, part (c) asks for the probability that a randomly selected Hispanic student did not receive a bachelor's degree. This probability is found by subtracting the number of bachelor's degrees from the total number of degrees. The calculation comes to \(P(No Bachelor's Degree) = \frac{274,515 - 129,526}{274,515}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Statistics in Education
Understanding statistics in education provides valuable insights into various educational outcomes, including degree completion rates among demographic groups. To compute probabilities using educational data, we begin with accurate collection and categorization of data. In our exercise, we analyzed the number of degrees awarded to Hispanic students in a particular academic year. This exercise in probability calculation is an application of descriptive statistics, a branch of statistics dealing with the analysis of data that provides a description of a sample.

Through educational statistics, stakeholders can make informed decisions based on patterns and trends. For example, when assessing the impact of different programs aimed at supporting Hispanic student success, statisticians would analyze data to determine their effectiveness. This helps schools and policymakers tailor educational strategies to meet the needs of various student populations.
Hispanic Student Degrees
Taking a specific look at the degrees awarded to Hispanic students, we can assess educational attainment within this demographic. By breaking down the types of degrees received—Associate, Bachelor's, and graduate or professional degrees—we can evaluate the educational landscape for Hispanic students. For instance, we can explore the accessibility and attractiveness of higher education among Hispanic students by examining the trends in degree attainment.

Taking the data from our exercise, there's a clear interest and achievement in both Associate and Bachelor's degrees among Hispanic students in the 2008-2009 academic year. Such analysis is crucial for universities and colleges in crafting programs and resources to further support Hispanic students to not only enter higher education but to successfully graduate with degrees that meet their personal and career objectives.
Academic Year Degree Analysis
In the context of our exercise, an academic year degree analysis refers to the study of all degrees conferred over an academic year. By assessing the probabilities of receiving different degrees, educational institutions can monitor students' progression and success rates. This year-over-year analysis can also reveal trends, such as shifts towards certain disciplines or changes in the popularity of graduate studies.

Such a comprehensive review guides schools in understanding trends and needs to possibly reassess their academic offerings. Forecasting future demand for programs and aligning resources to meet that demand is critical for ensuring that institutions remain responsive and relevant to student aspirations and societal needs. The probability calculations we conducted are part of this larger analytical process, underlining the importance of statistics in effectively managing and advancing educational programs.

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Most popular questions from this chapter

In a small city, approximately \(15 \%\) of those eligible are called for jury duty in any one calendar year. People are selected for jury duty at random from those eligible, and the same individual cannot be called more than once in the same year. What is the probability that an eligible person in this city is selected in both of the next 2 years? All of the next 3 years?

An electronics store sells two different brands of DVD players. The store reports that \(30 \%\) of customers purchasing a DVD choose Brand \(1 .\) Of those that choose Brand \(1,20 \%\) purchase an extended warranty. Consider the chance experiment of randomly selecting a customer who purchased a DVD player at this store. a. One of the percentages given in the problem specifies an unconditional probability, and the other percentage specifies a conditional probability. Which one is the conditional probability, and how can you tell? b. Suppose that two events \(B\) and \(E\) are defined as follows: \(B=\) selected customer purchased Brand 1 \(E=\) selected customer purchased an extended warranty Use probability notation to translate the given information into two probability statements of the form \(P(\underline{ })=\) probability value.

Suppose that an individual is randomly selected from the population of all adult males living in the United States. Let \(A\) be the event that the selected individual is over 6 feet in height, and let \(B\) be the event that the selected individual is a professional basketball player. Which do you think is larger, \(P(A \mid B)\) or \(P(B \mid A) ?\) Why?

Six people hope to be selected as a contestant on a TV game show. Two of these people are younger than 25 years old. Two of these six will be chosen at random to be on the show. a. What is the sample space for the chance experiment of selecting two of these people at random? (Hint: You can think of the people as being labeled \(\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}, \mathrm{E},\) and \(\mathrm{F}\). One possible selection of two people is \(\mathrm{A}\) and \(\mathrm{B}\). There are 14 other possible selections to consider.) b. Are the outcomes in the sample space equally likely? c. What is the probability that both the chosen contestants are younger than \(25 ?\) d. What is the probability that both the chosen contestants are not younger than \(25 ?\) e. What is the probability that one is younger than 25 and the other is not?

A rental car company offers two options when a car is rented. A renter can choose to pre-purchase gas or not and can also choose to rent a GPS device or not. Suppose that the events \(A=\) event that gas is pre-purchased \(B=\) event that a GPS is rented are independent with \(P(A)=0.20\) and \(P(B)=0.15\). a. Construct a "hypothetical 1000 " table with columns corresponding to whether or not gas is pre-purchased and rows corresponding to whether or not a GPS is rented. b. Use the table to find \(P(A \cup B)\). Give a long-run relative frequency interpretation of this probability.
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