Binomial Distribution: Choose CDF for "At Most 15 Students Play Sport" Probability

Question

A binomial probability density function should be used because the question asks for determining the probability that, at most, 15 students play a sport. A binomial probability density function should be used because the question asks for determining the probability that exactly 15 students play a sport. A binomial cumulative distribution function should be used because the question asks for determining the probability that at most, 15 students play a sport. A binomial cumulative distribution function should be used because the question asks exactly 25% of students play a sport, to determine the probability that, at most, 15 students play a sport. A binomial probability should not be used because the events are not independent of each other.

Accepted Answer

A binomial cumulative distribution function should be used because the question asks for determining the probability that at most, 15 students play a sport.

Answer

Step 1: Identify the core question: selecting 50 students with 25% sport participation, find the probability of at most 15 playing a sport. Step 2: Eliminate options that reference PDF, since PDF only calculates exact counts, not cumulative "at most" values. Step 3: Eliminate the option claiming binomial cannot be used: student selections are independent (random sample, large population assumption), so binomial is valid. Step 4: Select the option that correctly links "at most" to the cumulative distribution function, which sums probabilities from 0 to 15 successes.