In 2016, it was reported that 6% of all first-time mothers were 19 years old. Suppose a sample of 400 new mothers is chosen.

a. Describe the sampling distribution of the proportion of first-time mothers who were 19 years old for samples of 400.

b. Find the probability that the proportion of a sample of 400 first-time mothers that are 19 years old is less than 5%.

c. Find the probability that the proportion of a sample of 400 first-time mothers that are 19 years old is at least 6.25%.

d. Find the probability that the proportion of a sample of 400 first-time mothers that are 19 years old is at most 7%.

e. Find the probability that the proportion of a sample of 400 first-time mothers that are 19 years old is between than 6.5% and 7.5%.

f. Find the proportion of a sample of 400 first-time mothers that are 19 years old above which 15% of all proportions of samples of 400 first-time mothers that are 19 years old fall.

g. Find the proportion of a sample of 400 first-time mothers that are 19 years old below which 60% of all proportions of samples of 400 first-time mothers that are 19 years old fall.

h. Find the proportions of a sample of 400 first-time mothers that are 19 years old between which the middle 85% of all proportions of samples of 400 first-time mothers that are 19 years old fall