Suppose that for a recent admissions class, an Ivy League college received 2,825 applications for early admission. Of this group, it admitted 1,007 students early, rejected 854 outright, and deferred 964 to the regular admission pool for further consideration. In the past, this school has admitted 18% of the deferred early admission applicants during the regular admission process. Counting the students admitted early and the students admitted during the regular admission process, the total class size was 2,375. Let E, R, and D represent the events that a student who applies for early admission is admitted early, rejected outright, or deferred to the regular admissions pool. (a) Use the data to estimate P(E), P(R), and P(D). If required, round your answers to four decimal places. P(E)= .3565 P(R) = P(D) = .3023 (b) Are events E and D mutually exclusive? .3412 Yes Find P(En D). If your answer is zero, enter "0". .4240 (c) For the 2,375 students who were admitted, what is the probability that a randomly selected student was accepted during early admission? If required, round your answer to four decimal places. .4181 (d) Suppose a student applies for early admission. What is the probability that the student will be admitted for early admission or be deferred and later admitted during the regular admission process? If required, round your answer to four decimal places.
Suppose that for a recent admissions class, an Ivy League college received 2,825 applications for early admission. Of this group, it admitted 1,007 students early, rejected 854 outright, and deferred 964 to the regular admission pool for further consideration. In the past, this school has admitted 18% of the deferred early admission applicants during the regular admission process. Counting the students admitted early and the students admitted during the regular admission process, the total class size was 2,375. Let E, R, and D represent the events that a student who applies for early admission is admitted early, rejected outright, or deferred to the regular admissions pool. (a) Use the data to estimate P(E), P(R), and P(D). If required, round your answers to four decimal places. P(E)= .3565 P(R) = P(D) = .3023 (b) Are events E and D mutually exclusive? .3412 Yes Find P(En D). If your answer is zero, enter "0". .4240 (c) For the 2,375 students who were admitted, what is the probability that a randomly selected student was accepted during early admission? If required, round your answer to four decimal places. .4181 (d) Suppose a student applies for early admission. What is the probability that the student will be admitted for early admission or be deferred and later admitted during the regular admission process? If required, round your answer to four decimal places.
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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Transcribed Image Text:### Early Admission Process Analysis
Suppose for a recent admissions class, an Ivy League college received 2,825 applications for early admission. Of this group, it admitted 1,007 students early, rejected 854 outright, and deferred 964 to the regular admission pool for further consideration. In the past, this school has admitted 18% of the deferred early admission applicants during the regular admission process. Counting the students admitted early and the students admitted during the regular admission process, the total class size was 2,375. Let \( E, R, \) and \( D \) represent the events that a student who applies for early admission is admitted early, rejected outright, or deferred to the regular admissions pool.
#### (a) Probability Estimations
Use the data to estimate \( P(E) \), \( P(R) \), and \( P(D) \). If required, round your answers to four decimal places.
- \( P(E) = 0.3565 \) ✔️
- \( P(R) = 0.3023 \) ✔️
- \( P(D) = 0.3412 \) ✔️
#### (b) Mutual Exclusivity
Are events \( E \) and \( D \) mutually exclusive?
- **Answer**: Yes ✔️
Find \( P(E \cap D) \). If your answer is zero, enter "0".
- \( P(E \cap D) = 0 \) ✔️
#### (c) Probability of Early Admission Acceptance
For the 2,375 students who were admitted, what is the probability that a randomly selected student was accepted during early admission? If required, round your answer to four decimal places.
- Probability: \( 0.4240 \) ✔️
#### (d) Probability of Admission via Early or Deferred Process
Suppose a student applies for early admission. What is the probability that the student will be admitted for early admission or be deferred and later admitted during the regular admission process? If required, round your answer to four decimal places.
- Probability: \( 0.4181 \) ✖️
**Note**: The calculated probability in part (d) requires validation for accuracy.
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