ive hundred first-year students at a state university were classified according to both high school grade point average (GPA) and whether they were on academic probation at the end of their first semester. The data are summarized in the accompanying table. Probation High School GPA Total 2.5 to <3.0 3.0 to <3.5 3.5 and Above Yes 50 55 30 135 No 35 145 185 365 Total 85 200 215 500 (a) Use the given table to approximate the probability that a randomly selected first-year student at this university will be on academic probation at the end of the first semester. (b) What is the estimated probability that a randomly selected first-year student at this university had a high school GPA of 3.5 or above? (c) Are the two events selected student has a high school GPA of 3.5 or above and selected student is on academic probation at the end of the first semester independent events? How can you tell? Yes they are independent because P(GPA of 3.5 or above) · P(on probation) ≠ P(GPA of 3.5 or above ∩ on probation). Yes they are independent because P(GPA of 3.5 or above) · P(on probation) = P(GPA of 3.5 or above ∩ on probation). No they are not independent because P(GPA of 3.5 or above) · P(on probation) = P(GPA of 3.5 or above ∩ on probation). No they are not independent because P(GPA of 3.5 or above) · P(on probation) ≠ P(GPA of 3.5 or above ∩ on probation). (d) Estimate the proportion of first-year students with high school GPAs between 2.5 and 3.0 who are on academic probation at the end of the first semester. (Round your answer to three decimal places.)
ive hundred first-year students at a state university were classified according to both high school grade point average (GPA) and whether they were on academic probation at the end of their first semester. The data are summarized in the accompanying table. Probation High School GPA Total 2.5 to <3.0 3.0 to <3.5 3.5 and Above Yes 50 55 30 135 No 35 145 185 365 Total 85 200 215 500 (a) Use the given table to approximate the probability that a randomly selected first-year student at this university will be on academic probation at the end of the first semester. (b) What is the estimated probability that a randomly selected first-year student at this university had a high school GPA of 3.5 or above? (c) Are the two events selected student has a high school GPA of 3.5 or above and selected student is on academic probation at the end of the first semester independent events? How can you tell? Yes they are independent because P(GPA of 3.5 or above) · P(on probation) ≠ P(GPA of 3.5 or above ∩ on probation). Yes they are independent because P(GPA of 3.5 or above) · P(on probation) = P(GPA of 3.5 or above ∩ on probation). No they are not independent because P(GPA of 3.5 or above) · P(on probation) = P(GPA of 3.5 or above ∩ on probation). No they are not independent because P(GPA of 3.5 or above) · P(on probation) ≠ P(GPA of 3.5 or above ∩ on probation). (d) Estimate the proportion of first-year students with high school GPAs between 2.5 and 3.0 who are on academic probation at the end of the first semester. (Round your answer to three decimal places.)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
Related questions
Question
Five hundred first-year students at a state university were classified according to both high school grade point average (GPA) and whether they were on academic probation at the end of their first semester. The data are summarized in the accompanying table.
| Probation | High School GPA | Total | ||
|---|---|---|---|---|
| 2.5 to <3.0 | 3.0 to <3.5 | 3.5 and Above | ||
| Yes | 50 | 55 | 30 | 135 |
| No | 35 | 145 | 185 | 365 |
| Total | 85 | 200 | 215 | 500 |
(a)
Use the given table to approximate the probability that a randomly selected first-year student at this university will be on academic probation at the end of the first semester.
(b)
What is the estimated probability that a randomly selected first-year student at this university had a high school GPA of 3.5 or above?
(c)
Are the two events selected student has a high school GPA of 3.5 or above and selected student is on academic probation at the end of the first semester independent events? How can you tell?
Yes they are independent because
P(GPA of 3.5 or above) · P(on probation) ≠ P(GPA of 3.5 or above ∩ on probation).
Yes they are independent because
P(GPA of 3.5 or above) · P(on probation) = P(GPA of 3.5 or above ∩ on probation).
No they are not independent because
P(GPA of 3.5 or above) · P(on probation) = P(GPA of 3.5 or above ∩ on probation).
No they are not independent because
P(GPA of 3.5 or above) · P(on probation) ≠ P(GPA of 3.5 or above ∩ on probation).
(d)
Estimate the proportion of first-year students with high school GPAs between 2.5 and 3.0 who are on academic probation at the end of the first semester. (Round your answer to three decimal places.)
(e)
Estimate the proportion of those first-year students with high school GPAs of 3.5 and above who are on academic probation at the end of the first semester. (Round your answer to three decimal places.)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON