/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 18 The same issue of The Chronicle ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

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 \(P(No Bachelor's Degree) = \frac{274,515 - 129,526}{274,515}\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

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鈥擜ssociate, Bachelor's, and graduate or professional degrees鈥攚e 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.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

a. Suppose events \(E\) and \(F\) are mutually exclusive with \(P(E)=0.41\) and \(P(E)=0.23\). i. What is the value of \(P(E \cap F) ?\) ii. What is the value of \(P(E \cup F) ?\) b. Suppose that for events \(A\) and \(B, P(A)=0.26, P(B)=0.34\), and \(P(A \cup B)=0.47 .\) Are \(A\) and \(B\) mutually exclusive? How can you tell?

According to The Chronicle for Higher Education (Aug. 26, 2011), there were 787,325 Associate degrees awarded by U.S. community colleges in the \(2008-2009\) academic year. A total of 488,142 of these degrees were awarded to women. a. If a person who received an Associate degree in 2008 2009 is selected at random, what is the probability that the selected person will be female? b. What is the probability that the selected person will be male?

In an article that appears on the website of the American Statistical Association (www.amstat.org), Carlton Gunn, a public defender in Seattle, Washington, wrote about how he uses statistics in his work as an attorney. He states: I personally have used statistics in trying to challenge the reliability of drug testing results. Suppose the chance of a mistake in the taking and processing of a urine sample for a drug test is just 1 in \(100 .\) And your client has a "dirty" (i.e., positive) test result. Only a 1 in 100 chance that it could be wrong? Not necessarily. If the vast majority of all tests given - say 99 in 100 - are truly clean, then you get one false dirty and one true dirty in every 100 tests, so that half of the dirty tests are false. Define the following events as \(T D=\) event that the test result is dirty \(T C=\) event that the test result is clean \(D=\) event that the person tested is actually dirty \(C=\) event that the person tested is actually clean a. Using the information in the quote, what are the values of i. \(P(T D \mid D)\) iii. \(P(C)\) ii. \(P(T D \mid C)\) iv. \(P(D)\) b. Use the probabilities from Part (a) to construct a "hypothetical 1000 " table. c. What is the value of \(P(T D)\) ? d. Use the table to calculate the probability that a person is clean given that the test result is dirty, \(P(C \mid T D)\). Is this value consistent with the argument given in the quote? Explain.

The paper "Predictors of Complementary Therapy Use Among Asthma Patients: Results of a Primary Care Survey" (Health and Social Care in the Community [2008]: \(155-164)\) described a study in which each person in a large sample of asthma patients responded to two questions: Question 1: Do conventional asthma medications usually help your symptoms? Question 2: Do you use complementary therapies (such as herbs, acupuncture, aroma therapy) in the treatment of your asthma? Suppose that this sample is representative of asthma patients. Consider the following events: \(E=\) event that the patient uses complementary therapies \(F=\) event that the patient reports conventional medications usually help The data from the sample were used to estimate the following probabilities: $$P(E)=0.146 \quad P(F)=0.879 \quad P(E \cap F)=0.122$$ a. Use the given probability information to set up a "hypothetical 1000 " table with columns corresponding to \(E\) and \(n o t E\) and rows corresponding to \(F\) and not \(F\). b. Use the table from Part (a) to find the following probabilities: i. The probability that an asthma patient responds that conventional medications do not help and that patient uses complementary therapies. ii. The probability that an asthma patient responds that conventional medications do not help and that patient does not use complementary therapies. iii. The probability that an asthma patient responds that conventional medications usually help or the patient uses complementary therapies. c. Are the events \(E\) and \(F\) independent? Explain.

Each time a class meets, the professor selects one student at random to explain the solution to a homework problem. There are 40 students in the class, and no one ever misses class. Luke is one of these students. What is the probability that Luke is selected both of the next two times that the class meets? (Hint: See Example 5.8 )
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.