Solve PASCAL Math Homework - Help with Questions

[F.B]

I need help please with all these questions.

1. How many different paths on the diagram below will spell PASCAL?

* This diagram is a little wrong because i don't know how to do it on the forums, but anyways the letters should be spaced out so that they are in between each of the spaces.

P
A A
S S S
C C
A A A
L L

I count 16 if I do it manually, how do I do it as a combination my teacher never thought us how to do questions like these.

2. The mean age of 120 teachers in a school is 38 yrs old with a standard deviation of 5.3. Six of the teachers in the school are over 54 years of age. Is the distribution of the teachers’ age normal?

Heres what I did so can you please check it.

X~N(38,5.3)

=38+3(5.3)
=53.9
=0.15%

0.15% x 120=0.18

3. What are the possible values of n numbers if a set of n numbers always included its quartiles Q1, Q2, Q3?

3,7,11,15,19…..etc

tn=4n-1

Does this make sense? I think these are the right answers.

4. State the values of the first five powers of 11, starting with exponent 0, and compare these values to the entries in the first five rows of Pascal’s Triangle. Explain the relationship and why it fails for the next power of 11.

I am not sure what they are asking. But I think they want me to do this:

11^0=1 11^1=11 11^2=121 11^3=1331 11^4=14641 11^5=161,051

But now I don’t know what else to do so can you please help me.


So can anyone please help me with all these questions.

 

[cepheid]

You spell PASCAL by landing on a letter in each sequential row until you get to the bottom. So, I think you can agree that there is only one way to spell 'P', by starting at the beginning. And that there are only two ways to spell 'PA', by going down to one of each of the two A's. And FOR EACH of those two A's, you can go down to one of the three S's. So, I think you can see that that means that FOR EACH of the two PA paths, there are three possible S's to land on, leading to 3 x 2 possible paths in total. I kept capitalizing 'for each' to make it absolutely clear/emphasize why you would multiply. So I think you can see the pattern here? How to get down to the bottom?

If you like to think of it another way, in each row there are a certain number of letters. Say there are n letters in a row. To go down to that row, you have to choose one of those letters. nC1 = n. Same for the successive rows, multiplying all those terms together.

 

[HallsofIvy]

What exactly do you mean by a path? That is, if you go from the "P" to the first of the two "A" can you then go to the third "S" in the next row or only to one of the two "S" directly under that "A".

And if your teacher has taught you the "fundamental counting principle" then he/she HAS taught you how to do "questions like these". You are expected to THINK about how to apply principle to new problems.

2. The mean age of 120 teachers in a school is 38 yrs old with a standard deviation of 5.3. Six of the teachers in the school are over 54 years of age. Is the distribution of the teachers’ age normal?

Heres what I did so can you please check it.

X~N(38,5.3)

=38+3(5.3)
=53.9
=0.15%

0.15% x 120=0.18

You haven't answered the question have you? Exactly what does "0.18" represent and how does that help you answer the question?

3. What are the possible values of n numbers if a set of n numbers always included its quartiles Q1, Q2, Q3?

3,7,11,15,19…..etc

tn=4n-1

Does this make sense? I think these are the right answers.

I'm not sure I understand what you have done. WHY do you think these are the right answers?

4. State the values of the first five powers of 11, starting with exponent 0, and compare these values to the entries in the first five rows of Pascal’s Triangle. Explain the relationship and why it fails for the next power of 11.

I am not sure what they are asking. But I think they want me to do this:

11^0=1 11^1=11 11^2=121 11^3=1331 11^4=14641 11^5=161,051

But now I don’t know what else to do so can you please help me.

Certainly the next thing should be to do what is suggested: compare with the first 5 rows of Pascal's triangle. Then think about how (10+ 1)ⁿ is related to (x+ y)ⁿ.

 

[F.B]

For number 1 my teacher did tell us how to do use Permutations and combinations but i don't know how to apply it to this type of question because i have never done one before so if i were to do this instead for 1 would i be right.

To get PA there are 2 ways, to get PAS there are 4 ways, then to get PASC there are another 4 ways, to get PASCA there are once again 4 ways, finally to get PASCAL there are 4 ways again.
So now is my answer 2 x 4 x 4 x 4 x 4=512
But that number is way too much.
So how to do i apply these questions to Permulation/Combinations.

2. That 0.18 represents the distribution, since its under 1, that answer its not normal.

3. That equation i made satisfies what they are asking, if i write down 3 numbers then Q1,Q2 and Q3 are part of it. Then if u write 7 numbers again Q1,Q2 and Q3 are actual numbers.

4. So for 4 do i do (10+1)^0 , (10+1)^1 and so on and compare those number to my other numbers.