Question

Use the probability distribution graph to answer the question.

P(X≤a)=0.6

What is the value of a?

Graph:
https://static.k12.com/nextgen_media/assets/8078638-NG_AL2_SemA_01_UT_06.png

Answer 1

since P(X≤a) we need to find an X-value where the area of the curve is exactly 0.6 to the left of a

Answer 2

for example, if we let a = 1, the area to the left is:

Answer 3

so we would keep testing higher and higher X-values until we find an X-value where the area to the left of that value is exactly 0.6

lmk if you get stuck or want to check your answer

Answer 4

ahhh ty for coming to the rescue lol i was stuck on this question all morning

Answer 5

wait so which value do i need to test next?

Answer 6

@Vocaloid

Answer 7

well, since 1 was way too low, try jumping up to 4 or 5

Answer 8

would it be 0.2*0.05?

Answer 9

if you're testing X = 4, then we'd want the area of this triangle, which is (1/2)(base)(height) = ?

Answer 10

4x4? times 1/2?

Answer 11

wait idk

Answer 12

base is 4

Answer 13

height is 0.2

Answer 14

area = (1/2)(0.2)*4 = 0.4, we're still a little short, try calculating the total area to the left of X = 5

Answer 15

as a hint, it's the sum of the previous triangle we calculated plus a small rectangle

Answer 16

1/2*0.25*5? that would be 0.625

Answer 17

keep in mind the area to the left of X = 5 is not just one triangle, it's a triangle + a rectangle

Answer 18

what's the area of this rectangle?

Answer 19

ehmm base = 1? i'm not sure about that and then height = 0.2 and that times 1/2 = 0.1

Answer 20

for a rectangle, it's just base * height, there's no 1/2

Answer 21

so base * height = 1 * 0.2 = 0.2

adding that to the triangle from before, 0.2 + 0.4 = 0.6, so the probability of X <= 5 is 0.6, making our value of a = 5 = your answer

Answer 22

ohh okay, that makes more sense than what i did. thanks again