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alisha [4.7K]
4 years ago
9

Math workshops and final exams: The college tutoring center staff are considering whether the center should increase the number

of math workshops they offer to help students improve their performance in math classes. Faculty would like to know if requiring student attendance at these math workshops will improve overall passing rates for their students in their math classes. They plan to use the number of workshops attended to predict the final exam score and regression analysis to determine the effectiveness of the mandatory workshop attendance policy. Which is the response variable?
1. Whether the student attended a workshop.
a. yes.
b. no.
2. Number of workshops attended.
3. Whether the student passes the course.
a. yes.
b. no.
4. Final exam score Correlation.
Mathematics
1 answer:
ludmilkaskok [199]4 years ago
3 0

Answer:

2. Number of workshops attended.

Step-by-step explanation:

The variable of interest for predicting the final exam score and doing regression analysis is workshop attendance.  Therefore, the response variable should be the number of workshops attended by each student.

This also agrees with what the college tutoring center staff are considering, which forms the research question: "should the center increase the number of math workshops they offer to help students improve their performance in math classes?"

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Using the binomial distribution, it is found that there is a 0.0328 = 3.28% probability that at least 2 of them choose the same quote.

<h3>What is the binomial distribution formula?</h3>

The formula is:

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

C_{n,x} = \frac{n!}{x!(n-x)!}

The parameters are:

  • x is the number of successes.
  • n is the number of trials.
  • p is the probability of a success on a single trial.

In this problem, we have that:

  • There are 6 students, hence n = 6.
  • There are 20 quotes, hence the probability of each being chosen is p = 1/20 = 0.05.

The probability of one quote being chosen at least two times is given by:

P(X \geq 2) = 1 - P(X < 2)

In which:

P(X < 2) = P(X = 0) + P(X = 1).

Then:

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{6,0}.(0.05)^{0}.(0.95)^{6} = 0.7351

P(X = 1) = C_{6,1}.(0.05)^{1}.(0.95)^{5} = 0.2321

Then:

P(X < 2) = P(X = 0) + P(X = 1) = 0.7351 + 0.2321 = 0.9672.

P(X \geq 2) = 1 - P(X < 2) = 1 - 0.9672 = 0.0328

0.0328 = 3.28% probability that at least 2 of them choose the same quote.

More can be learned about the binomial distribution at brainly.com/question/24863377

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