Final answer:
To find the probability that the sample proportion of baseball players is greater than 55%, calculate the standard deviation of the sampling distribution and determine the z-score for a sample proportion of 55%. Then, use a standard normal distribution to find the probability for this z-score.
Step-by-step explanation:
The question asks about the probability of having a sample proportion of baseball players greater than 55% when 58% of the students in a university are baseball players. The Central Limit Theorem can be applied here since the sample size is large (n=681). We first find the standard deviation of the sampling distribution (σ_p’ = √[p(1-p)/n]) and then compute the z-score for the sample proportion of 55% using the formula z = (p’ - p)/σ_p’, where p’ is the sample proportion (0.55) and p is the population proportion (0.58). After calculating the z-score, we look up this value in the standard normal distribution table or use a calculator function (like normalcdf on a TI-83/84) to find the probability that the z-score is greater than the calculated value, which would give us the probability that the sample proportion is greater than 55%. Since this question involves statistical methods to estimate a probability, it requires the usage of a calculator with statistical functions, as noted in the instructions.