Question

I am willing to work. I want to learn.
Topic: Algebra II
I will upload questions once thread is open. Thanks.

Answer 1

The graph shows a probability distribution.
Which probabilities are equal to 0.5?
SELECT ALL THAT APPLY

What I do know:

• P(5≤X≤7)

This one is rather easy. (At least I hope it is !)

Referencing the figure we would draw our line from 5 to 7 creating a rectangle. From there we would utilize the formula for a rectangle to get…

A = 4 X 2 = 8

8 is NOT equal to 0.5, so we can rule it out.

• P(X≤5)

This gives us the shape of a triangle. This time we would use the formula for a triangle.

A = 5 X 0.2 / 2 = 0.5

0.5 is equal to 0.5 !

• P(X≥7)

Another triangle another formula for a triangle.

A = 1 X 0.2 / 2 = 0.1

0.1 DOES NOT EQUAL 0.5, so we can rule it out.

• P(X≥5)
I’m a little confused on this one. It seems to take the shape of a trapezoid, but…?

I would appreciate any opinions or advice one may have…

Answer 2

First of all: The area under a probability distribution curve MUST be 1. Is that true of the given probability distribution?

I applaud you for providing so much info regarding your thinking. However, you and y our helper(s) might get mor done if you'd post one question at a time, e. g., "P(5≤X≤7)"

Show how you'd find this probability and what result you obtain. Then move on to a new question.

Example: Is\[P(5≤X≤7)\] equal to 0.5?

Width of area in question is 2 units. This area is a rectangle of uniform height 0.2. Thus, its area is (0.2)(2)=0.4. No, this probability is NOT 0.5.

Move on to the next question now.

Answer 3

To answer the first question our probability distribution IS equal to 1. I will not take your advice and answer one question at a time. Thank you for replying!

Answer 4

P(X≤5)

Looking at the graph, I see the formation of a triangle. Would you agree? If so, we would 'plug in' the correct information into the formula for a triangle.

A = 5 X 0.2 / 2 = 0.5

0.5 is equal to 0.5 ! So I would say yes on this one. Correct me if I am wrong though !

Answer 5

We will call the above the SECOND question, as to not get confused. I shall now move on to the THIRD question where I will pause for responses. I hope that's not too confusing.

Answer 6

THIRD QUESTION

P(X≥7)

This seems to form another triangle. That being said we would use the formula for a triangle once more.

A = 1 X 0.2 / 2 = 0.1

0.1 DOES NOT EQUAL 0.5.

Answer 7

@mathmale Would you agree with my work? (I by no means mean to rush you).

Answer 8

While the educated person can guess what you mean by A = 1 X 0.2 / 2 = 0.1, greater clarity would be appreciated. You might state that you're using the formula for the area of a triangle, which ought to be written as\[A _{\triangle}=\frac{ bh }{ 2}.\] I do agree with your result (A=0.1). True, that does not equal 0.5.

Move on to the next problem, please.