At a certaincollege, 52% of employees carry dependent family members on their health insurance plans.Currently, there are 200 employees working for the college. A random sample of 60 employees is selected. Complete parts a through c below.

a. What is the probability that less than 57% of the sample carries dependent family members on their health insuranceplan?

P(less than 57% of the sample carries dependent family members) =

(Round to four decimal places asneeded.)

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 57% of the sample carries dependent family members)=

(Round to four decimal places asneeded.)

Find the probability for a sample size of 150

P(less than 57% of the sample carries dependent family members)=

(Round to four decimal places asneeded.)

Explain the differences in these probabilities. Choose the correct answer below.

A.Increasing the sample size reduces the standard error.This, inturn, increases the probabilities that the sample proportions will be closer to the population proportion.

B.Increasing the sample size increases the standard error.This, inturn, increases the probabilities that the sample proportions will be closer to the population proportion.

C.Increasing the sample size reduces the standard error.This, inturn, decreases the probabilities that the sample proportions will be closer to the population proportion.

D.Increasing the sample size increases the standard error.This, inturn, decreases 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 57% of the sample carries dependent family members)=

(Round to four decimal places asneeded.)

Explain the differences in these probabilities. Choose the correct answer below.

A.Without the finite correctionfactor, the standard error isoverestimated, causing the probability to be overestimated.

B.Without the finite correctionfactor, the standard error isoverestimated, causing the probability to be underestimated.

C.Without the finite correctionfactor, the standard error isunderestimated, causing the probability to be overestimated.

D.Without the finite correctionfactor, the standard error isunderestimated, causing the probability to be underestimated.