6. Past data for new students in the College of Business at State U show 23.5% enroll as accounting majors, 12.5% are required to complete a developmental math course upon enrollment, and 2.8% fall into both categories. (c) How many business students would we expect to select before choosing the first accounting major? Interpret the result. (d) In a random group of 40 newly-enrolled business students, what is the probability from 2 to 6 are required to complete a developmental math course?
6. Past data for new students in the College of Business at State U show 23.5% enroll as accounting majors, 12.5% are required to complete a developmental math course upon enrollment, and 2.8% fall into both categories. (c) How many business students would we expect to select before choosing the first accounting major? Interpret the result. (d) In a random group of 40 newly-enrolled business students, what is the probability from 2 to 6 are required to complete a developmental math course?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question 6.2
Please solve the problem with simple probability rules (no Excel)
![### Enrollment Statistics in the College of Business at State U
Past data for new students in the College of Business at State U show the following statistics:
- 23.5% enroll as accounting majors.
- 12.5% are required to complete a developmental math course upon enrollment.
- 2.8% fall into both categories (accounting majors who need a developmental math course).
#### (a-d) Problem Analysis
**(c) Expected Selection Before Choosing the First Accounting Major**
**Question:**
*How many business students would we expect to select before choosing the first accounting major? Interpret the result.*
**Solution:**
- To find the expected number of students to select before choosing the first accounting major, we use the concept of expectation in probability.
- The probability (p) of selecting an accounting major is 0.235 (23.5%).
The formula for the expected number of trials to achieve the first success (accounting major) in a geometric distribution is given by:
\[ E(X) = \frac{1}{p} \]
So,
\[ E(X) = \frac{1}{0.235} \approx 4.26 \]
**Interpretation:**
- On average, we would expect to select about 4.26 (approximately 4 to 5) business students before choosing the first accounting major.
**(d) Probability of Developmental Math Course Requirement in a Random Group**
**Question:**
*In a random group of 40 newly-enrolled business students, what is the probability from 2 to 6 are required to complete a developmental math course?*
**Solution:**
- To determine this probability, we can use the binomial probability formula, which is suitable for finding the probability of a specific number of successes in a fixed number of trials.
- Here, the trials are the 40 students, and the probability (p) that a student needs a developmental math course is 0.125 (12.5%).
The binomial probability formula is given by:
\[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \]
Where:
- \( n \) is the number of trials (40 students),
- \( k \) is the number of successes (students requiring a developmental math course, from 2 to 6),
- \( p \) is the probability of success (0.125).
To](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1d41a808-d0ca-407a-8825-29dbf8dd80d4%2F294f6864-078a-4c8e-b8f1-e46a92e54a2b%2F4d16uo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Enrollment Statistics in the College of Business at State U
Past data for new students in the College of Business at State U show the following statistics:
- 23.5% enroll as accounting majors.
- 12.5% are required to complete a developmental math course upon enrollment.
- 2.8% fall into both categories (accounting majors who need a developmental math course).
#### (a-d) Problem Analysis
**(c) Expected Selection Before Choosing the First Accounting Major**
**Question:**
*How many business students would we expect to select before choosing the first accounting major? Interpret the result.*
**Solution:**
- To find the expected number of students to select before choosing the first accounting major, we use the concept of expectation in probability.
- The probability (p) of selecting an accounting major is 0.235 (23.5%).
The formula for the expected number of trials to achieve the first success (accounting major) in a geometric distribution is given by:
\[ E(X) = \frac{1}{p} \]
So,
\[ E(X) = \frac{1}{0.235} \approx 4.26 \]
**Interpretation:**
- On average, we would expect to select about 4.26 (approximately 4 to 5) business students before choosing the first accounting major.
**(d) Probability of Developmental Math Course Requirement in a Random Group**
**Question:**
*In a random group of 40 newly-enrolled business students, what is the probability from 2 to 6 are required to complete a developmental math course?*
**Solution:**
- To determine this probability, we can use the binomial probability formula, which is suitable for finding the probability of a specific number of successes in a fixed number of trials.
- Here, the trials are the 40 students, and the probability (p) that a student needs a developmental math course is 0.125 (12.5%).
The binomial probability formula is given by:
\[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \]
Where:
- \( n \) is the number of trials (40 students),
- \( k \) is the number of successes (students requiring a developmental math course, from 2 to 6),
- \( p \) is the probability of success (0.125).
To
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