Final answer:
The probability that at least 3 but no more than 5 students will withdraw from a class with a 25% withdrawal rate and 16 students can be found using the binomial probability formula, summing the probabilities for each of the number of withdrawals from 3 to 5.
Step-by-step explanation:
The question involves finding the probability that at least 3 but no more than 5 students will withdraw from an introductory statistics class, given that the historical data shows a 25% withdrawal rate and 16 students have registered for the class. This can be solved using the binomial probability formula:
P(X = k) = C(n, k) * p^k * (1 - p)^(n - k),
where:
- C(n, k) is the combination of n items taken k at a time
- p is the probability of a single success
- n is the total number of trials
- k is the number of successes
In this case, n is 16 (the number of students), p is 0.25 (the probability of a student withdrawing), and k can be 3, 4, or 5. We have to calculate the probability for each value of k and then add them up to get the total probability for at least 3 but no more than 5 students withdrawing.
For k = 3:
P(X = 3) = C(16, 3) * (0.25)^3 * (0.75)^(16 - 3)
For k = 4:
P(X = 4) = C(16, 4) * (0.25)^4 * (0.75)^(16 - 4)
For k = 5:
P(X = 5) = C(16, 5) * (0.25)^5 * (0.75)^(16 - 5)
The total probability is the sum of the probabilities for k = 3, k = 4, and k = 5. This can be calculated using a calculator or any software that can compute binomial probabilities.
The subject at hand can be broadly categorized under the topics of binomial distribution and probability theory, which are core components of introductory statistics courses.