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Q: Math question about High School GPA ( No Answer,   1 Comment )
Question  
Subject: Math question about High School GPA
Category: Science > Math
Asked by: scifinut69-ga
List Price: $10.00
Posted: 20 Oct 2004 03:38 PDT
Expires: 20 Oct 2004 13:49 PDT
Question ID: 417446
The high school GPA of applicants for admission to a college program
are recorded and relative frequencies are calculated for the
categories.

			GPA			        f(x)

			x  <  2.0			.08
		 2.0 <=	x  <  2.5			.12   
		 2.5 <=	x  <  3.0			.35
		3.0  <=	x  <  3.5			.30
		3.5  <=	x				

	a.	Complete the table to make this a valid probability distribution.
	b.	What is the probability an applicant's GPA will be below 3.0?
	c.	What is the probability an applicant's GPA will be 2.5 or above?
Answer  
There is no answer at this time.

Comments  
Subject: Re: Math question about High School GPA
From: padmapani-ga on 20 Oct 2004 05:34 PDT
 
Firstly note the fact that the GPA cannot be more than 4.0 and that
the probabilities add upto 1.
(a) Noting this s you can fill out the last column's f(x) as 1
-(0.08+0.12+0.35+0.30) = 0.15. So you have the final distribution as

	         x  <  2.0			        .08
		 2.0 <=	x  <  2.5			.12   
		 2.5 <=	x  <  3.0			.35
		3.0  <=	x  <  3.5			.30
		3.5  <=	x  < 4.0 			.15	
(b) The relative frequency is the probability you are looking for.
So Pr( GPA < 3.0) =  Pr (0 < GPA < 3) = 0.08 + 0.12 + 0.35 = 0.55  or 55%.

(c) The same logic as above applies.
Pr(GPA > 2.5) = Pr (2.5 < GPA <= 4.0) = 0.35+0.30+0.15 = 0.80 or 80%

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