Math Problem Statement

Which probability is relevant for determining whether 6 is a significantly high number of girls in 8​ births: the result from part​ (a) or part​ (b)?

A.

The result from part​ b, since it is the complement of the result of part a.

B.

The result from part​ a, since it less than the probability of the given or more extreme result.

C.

The result from part​ b, since it is the probability of the given or more extreme result.

D.

The result from part​ a, since it is the exact probability being asked.

Solution

The correct answer is:

C. The result from part​ b, since it is the probability of the given or more extreme result.

Explanation: When determining whether a particular result is significantly high (in this case, 6 girls in 8 births), we typically look at the probability of obtaining that result or a more extreme one. In probability theory, for a result to be "significantly high," the probability of that result or a higher one must be relatively small.

Part b likely represents the probability of getting 6 or more girls (the given result or more extreme), which is essential for making this determination. Hence, part b is relevant.

Do you have any other questions about this or would you like further details?

Related questions:

  1. What is the probability of exactly 6 girls in 8 births?
  2. How do you calculate the cumulative probability for 6 or more girls in 8 births?
  3. What defines a significantly high result in terms of probability?
  4. How does the complement rule apply in determining probabilities of extreme events?
  5. What is the relationship between binomial distributions and these kinds of probability problems?

Tip: A result is considered "significantly high" if the probability of that result or anything more extreme is less than 5%.

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Math Problem Analysis

Mathematical Concepts

Probability
Binomial Distribution
Significance Testing

Formulas

P(X = k) = C(n, k) * p^k * (1-p)^(n-k) (Binomial Probability Formula)
P(X ≥ k) = 1 - P(X < k) (Cumulative Probability)

Theorems

Complement Rule
Binomial Theorem

Suitable Grade Level

Grades 9-12