+0  
 
0
69
4
avatar+180 


For the probability distribution shown, what 

is p(3 <  x < 6) ?

0.25


0.3


0.45


0.9

 Feb 17, 2020
edited by jj88778  Feb 17, 2020
edited by jj88778  Feb 17, 2020
edited by jj88778  Feb 17, 2020
edited by jj88778  Feb 17, 2020
 #1
avatar+180 
+1

****What is p(3 <  x < 6) ?

 Feb 17, 2020
edited by jj88778  Feb 17, 2020
edited by jj88778  Feb 17, 2020
 #2
avatar+18976 
+1

You need to find the area of the trapezoid whose "height" goes from 2.5 to 3.5 and whose midline has a length of 0.10. 

Area  =  base · midline  =  1 · 0.10  =  0.10

 

Unfortunately, I don't find that answer.

 Feb 17, 2020
 #3
avatar+180 
+1

I meant to put what is p(3 <  x < 6) ?

jj88778  Feb 17, 2020
 #4
avatar+108776 
+1

Hi JJ

The area of that whole triangle is    0.5*10*0.2 = 1   

It equals 1!  This is very significant. The area under a probability graph MUST equal 1.

 

P(3 <  x < 6) 

means what is the probability that the value (x) will lay between 3 and 6.

You can find that by finding the area of the shaded region that is between 3 and 6.

 

So that would be 

P(3 <  x < 6) =1 - the region in front where x is less than 3 - the region there x is bigger than 6

P(3 <  x < 6) =1 -                     0.5*3*0.1                              -                    0.5*4*0.2

P(3 <  x < 6) =1 -                         0.15                                  -                           0.4

P(3 <  x < 6) =  0.45

 

OR

 you could have done it as a trapezium, like Geno did.

P(3 <  x < 6) = 0.5(0.1+0.2)*3

P(3 <  x < 6) =0.45

 

Geno just made a careless error - we all do that sometimes.

 

I hope that helps. I think these concepts are hard to work out. I remember struggling with them. wink

Melody  Feb 17, 2020

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