Homework 21 In A Statistics Class Of 30 Students

Homework 21 In A Statistics Class Of 30 Students There Were 13 Men A

In a statistics class consisting of 30 students, the distribution includes 13 men and 17 women. Within this class, two men and three women received an A grade. A student is randomly selected from the class. The following problems are to be addressed:

1. Calculate the probability that the selected student is a woman.
2. Calculate the probability that the student received an A in the course.
3. Determine the probability that the student is a woman or received an A.
4. Find the probability that the student did not receive an A.

Paper For Above instruction

The statistical analysis of the class composition and performance provides insightful data pertinent to understanding the distribution of grades among students segmented by gender. The initial problem involves calculating simple probabilities based on the ratio of women in the class, the number of A grades awarded, and the combined likelihoods involving gender and grades.

First, the probability that a randomly selected student is a woman can be directly derived from the ratio of women in the class. Since there are 17 women out of 30 students, this probability (P(W)) is:

P(W) = 17/30 ≈ 0.567

Next, to determine the probability that the student received an A (P(A)), it is necessary to consider the total number of students who received A grades, regardless of gender. The data indicates three women and two men received an A, summing to five students. Therefore, P(A) is:

P(A) = 5/30 ≈ 0.167

For the third problem, which involves the probability that the student is a woman or received an A, the inclusion-exclusion principle is employed. The probability that a student is a woman or received an A (P(W ∪ A)) is given by:

P(W ∪ A) = P(W) + P(A) - P(W ∩ A)

The intersection, P(W ∩ A), refers to the probability that a student is both a woman and received an A. With three women receiving an A out of 30 students, this probability is:

P(W ∩ A) = 3/30 = 0.10

Substituting the known values, we get:

P(W ∪ A) = 0.567 + 0.167 - 0.10 = 0.634

Finally, the probability that a student did not receive an A (P(not A)) is the complement of the probability that the student received an A:

P(not A) = 1 - P(A) = 1 - 0.167 = 0.833

These calculations highlight the application's basic principles of probability, including the use of ratios, the inclusion-exclusion principle, and complementary probabilities. Understanding such distributions is fundamental in educational data analysis, enabling educators to make data-driven decisions regarding student performance and targeted interventions.

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