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.)

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

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ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter5: A Survey Of Other Common Functions

Section5.3: Modeling Data With Power Functions

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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.)

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