Final answer:
To find the probability that the sample proportion of baseball players will be less than 55%, use the normal approximation to the binomial distribution.
Step-by-step explanation:
To find the probability that the sample proportion of baseball players will be less than 55%, we can use the normal approximation to the binomial distribution. First, we need to find the mean and standard deviation of the sample proportion. The mean, μ, is equal to the population proportion, which is 56%, multiplied by the sample size, which is 873. So, μ = 0.56 * 873 = 488.08. The standard deviation, σ, is equal to the square root of (p*(1-p)/n), where p is the population proportion and n is the sample size. So, σ = sqrt(0.56*(1-0.56)/873) ≈ 0.0186.
Next, we can use the normal distribution to find the probability that the sample proportion will be less than 55%. We standardize the value 0.55 using the formula z = (x - μ) / σ, where x is the value we want to find the probability for. In this case, x = 0.55. So, z = (0.55 - 0.56) / 0.0186 ≈ -0.0538.
Finally, we can look up the probability for a z-score of -0.0538 in the standard normal distribution table or use a calculator to find the cumulative probability. The probability that the sample proportion will be less than 55% is approximately 0.2121, or 21.21%.