+0

0
69
4
+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
+180
+1

****What is p(3 <  x < 6) ?

Feb 17, 2020
edited by jj88778  Feb 17, 2020
edited by jj88778  Feb 17, 2020
#2
+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
+180
+1

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

jj88778  Feb 17, 2020
#4
+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.

Melody  Feb 17, 2020