Question

how do I figure this out?

The weights X of an animal are distributed according to the probability distribution shown.

What is the probability that the animal's weight will be less than 151 pounds?



0.25

0.50

0.60

0.75

Answer 1

I did this and got 0.60

Answer 2

ok, but how did you get that answer?

Answer 3

That is a uniform distribution

to find the probability of less than 151
find the area of the distribution that is less than 151
(area is length*width)
then divide by the total area of the entire distribution.

Answer 4

how do i know how to figure out what the length and width are?

Answer 5

The height of the rectangle is chosen so that the total area = 1
The width is 152-148 = 4
so we make the height ¼

Answer 6

now find the area of the rectangle with width (151-148)
and height 1/4

Answer 7

im not understanding this at all

Answer 8

ok.
The idea is this:
you have the whole rectangle.
you throw a dart at the rectangle.
what is the chance it hits in the part of the rectangle < 151 ?

Answer 9

i have no idea

Answer 10

we assume it's equally likely the dart hits anywhere in the rectangle.

the bigger the "target" area, the bigger the chances of hitting it.

Based on the numbers at the bottom, do you see the rectangle is 4 "units" wide ?

Answer 11

Do you see the 148, 149, etc ?

Answer 12

ok yes i see what youre saying!!

Answer 13

if we set the height of the rectangle to ¼
(and we see it's width is 4 "units" wide -- you can count the steps, or figure 152-148)
then the total area is 1 (we want the total area to represent the probability, and 1 means 100%)

the area of the rectangle less than 151 is 3 units wide
using the height ¼
we get 3*¼ = ¾
that is the probability of being less than 151

Answer 14

if we did not know the height of the rectangle, we can form the ratio of "area of target" divided by area of total rectangle.

we could call the height "y" (some unknown number)
and the ratio of areas would be
\[ \frac{3\cdot y}{4\cdot y} \]
the y's cancel, and we get
\[ \frac{3}{4} \]
which is the chance of being less than 151

Answer 15

okay, i think i understand that besides 1 part. how did you get 1/4? like how do you know thats the height?

Answer 16

area of a rectangle is A= L*W

we want the area to be 1
we know the width is 4
using that info we write:
1= 4*L
solve for L: divide both sides by 4
we get
¼ = L

I guess Length is not the right letter, but we know it stands for height in this case.

Answer 17

oh okay. thank you so much