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The graph shows a probability distribution.

Which probabilities are equal to 0.25?

P(X≥5)

P(3≤X≤4)

P(X≤2)

P(2≤X≤3)

 

The graph shows a probability distribution.

What is P(X<3)?

0.25

0.3

0.375

0.6

 Mar 12, 2018
 #1
avatar+101746 
+2

First one....we have a trapezoid.....

The area of a trapezoid  is

height/ 2 * ( sum of base lengths)

So we have......

.25 / 2  *  ( 6 + 2)  =  8/8   =    1  unit^2

And we are looking for areas =  .25 of this  =1/4 of this  =  .25   units^2

 

P( x ≥ 5)  =   area of a triangle with base = 1  and height  .25/2

Area  (1/2)base * height  =  (1/2) * 1 (.25 /2)  = .25/ 4  =  .0625  No

 

P ( 3 ≤ x ≤ 4)  = Area of rectangle = .25 * 1  = .25    Yes     (1)

 

P (  x ≤2 )  = Triangle with base of 2 and height of .25  =

(1/2)(2) * .25  =   .25  Yes

 

P ( 2 ≤ x ≤ 3)....same area as (1)   =  .25

 

So....only  the first answer is incorrect 

 

 

cool cool cool

 Mar 12, 2018
 #2
avatar+101746 
+2

Area of trapezoid  =

height / 2  * (sum of base lengths) =

(2/10) / 2 * ( 8 + 2)  =

(2/20) * 10   =

20/20  =  

1 square unit   = Total Area

 

P ( x  ≤ 3)  

We have a trangle with  a height of (2/10)  and base = 3

Area  = (1/2)(3)(2/10)  = 3 / 10

 

So....P ( x  ≤ 3)    =   ( Area of triangle) / (Total Area )  =

 

(3/10) / 1  =   3/10 =   0.3

 

 

cool cool cool

 Mar 12, 2018

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