At a certain college, 54% of employees carry dependent family members on their health insurance plans. Currently, there are 175 employees working for the college. A random sample of 50 employees is selected. Complete parts a through c below. 1 . . a. What is the probability that less than 58% of the sample carries dependent family members on their health insurance plan? P(less than 58% of the sample carries dependent family members) = (Round to four decimal places as needed.) b. Answer the question in part a using sample sizes of 100 and 150. Explain the differences in these probabilities. First find the probability for a sample size of 100. P(less than 58% of the sample carries dependent family members) = (Round to four decimal places as needed.) Find the probability for a sample size of 150. P(less than 58% of the sample carries dependent family members) = (Round to four decimal places as needed.)Explain the differences in these probabilities. Choose the correct answer below. 0 A. Increasing the sample size reduces the standard error. This. in tum, increases the probabilities that the sample proportions will be closer to the population proportion. O B. Increasing the sample size increases the standard error. This, in turn. decreases the probabilities that the sample proportions will be closer to the population proportion. O C. Increasing the sample size reduces the standard error. This. in tum, decreases the probabilities that the sample proportions will be closer to the population proportion. O D. Increasing the sample size increases the standard error. This, in turn. increases the probabilities that the sample proportions will be closer to the population proportion. c. Answer the question in part a without the finite correction factor. Explain the differences in these probabilities. P(less than 58% of the sample carries dependent family members) = (Round to four decimal places as needed.) Explain the differences in these probabilities. Choose the correct answer below. O A. Without the finite correction factor, the standard error is overestimated, causing the probability to be overestimated. O B. Without the finite correction factor, the standard error is overestimated, causing the probability to be underestimated. O C. Without the finite correction factor, the standard error is underestimated, causing the probability to be overestimated. O D. Without the finite correction factor, the standard error is underestimated, causing the probability to be underestimated