What is the probability of each being on top of the pyramid this week?

Chloe

Maddie

Chloe

Chloe

Maddie

Maddie

Because the studio is attending a New York competition this upcoming weekend, Abby must assign solos, duets, and trios. The odds in favour that Brooke will be in a duet are 1:7 and the probability that she gets a solo is 1/3. If Brooke DOES get a duet, the probability that fellow acrobatic dancer, Mackenzie, will be in the SAME duet is 3/4.

What is the probability that they will be in the same duet?

Before dismissing the parents and the girls from 'pyramid', because the parents were right there, she asks them to take a survey about their satisfaction at the studio. Abby finds that the results don't seem very accurate.

What kind of sampling did Abby use? Why is this sampling not always the best? What type of sampling should she use to generate more accurate results for next time?

The mothers are in charge of making the costumes for the group number this week for the competition. They are given a list of tasks to complete and have estimated how long each will take. They are looking for the quickest way to complete the costumes while ensuring all prerequisite tasks are completed.

During the group dance rehearsals, Abby isn't sure what combination of lines to organize the girls. She wants a line of 2, then a line of 3, and then another line of 2.

How many different possibilities are there for the girls to be organized in these lines if order of the girls doesn't matter?

The competition is coming up and all of Abby Lee Dance Company is heading to New York.

Abby must figure out how many students are attending so she can organize the proper accommodation and travel for the dancers as well as how many are doing what so she can enter it in the competition papers. She only knows the following information:

17 students are doing solos

21 students are doing a duet or trio

39 students are in a group number

12 students are doing both a solo and a group number

5 students are doing both a solo and a duet/trio

8 students are doing a duet/trio and are in a group number

4 students are doing all three

Abby decides to make a venn diagram to help her figure out the total number of kids entering in the competition.

When everyone arrives at the competition, they find their rivals, Candy Apples Dance Centre, is at the same competition! The team doesn't want to run into their rivals on the way to the stage from their dressing room and doesn't want to cross through their territory to avoid fights between the moms.

How many routes can they take to get to the stage and avoid their rivals?

After the awards presentation at the competition, Abby found the scores out of 300 of the top 10 girls in Maddie, Chloe, and Kendall's solo category. They are as followed:

KENDALL - 275.6, MADDIE - 298.5, CHLOE - 291.9, DANIELLE - 274.2, LAUREN - 284.9, SARAH - 289.7, CHRISTINA - 277.3,

JULIE - 285.2, HELEN - 279.8, KELLY - 280.1

Abby wants to know what the mean score was for the top 10 so she knows how successful her own dancers were in the competition. She also wants to know if any of the scores are outliers to see how far off the rest of the competition in the top 10 might have been.

In the dressing room after the competition, Christi (Chloe's mom) is upset about how she thinks Abby always favourites Maddie. She thinks that Maddie is always given more time for her solo more than anyone else. She collects data from all of the moms about how much time their daughters were given for their solos this week and put them against the solo scores from this weeks' competition.

Christi wants to know if there is a correlation between the time ABBY spends on their solos and their solo scores. She also wants to know how strong this correlation is in order to prove Abby isn't being fair.

Christi wants to confront Abby because of the correlation she found. Even though Christi can prove this correlation, the other moms warn her that Abby could bring up other things that may contribute to each dancer's individual scores.

What kind of extraneous variables are the moms talking about that Christi should consider?

After the competition, Abby parts with the girls, reminding them of her motto that "everyone is replaceable", just to ensure her dancers always stay on their game. This is because after large competitions like the one they just attended in New York, 9% of the dancers at the competition contact her with interest in coming to her company.

If 75 dancers are randomly selected from the competition, Abby wants to know the probability that at least 10 of the dancers will contact her post competition so she can set up auditions.

**nia**

**kendall**

**brooke**

**paige**

**mackenzie**

**chloe**

**maddie**

**kelly**

**jill**

**holly**

**melissa**

**christi**

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