The Wall Street Journal reported that the age at first startup for 55% of entrepreneurs was 29

Question:

The Wall Street Journal reported that the age at first startup for 55% of entrepreneurs was 29 years of age or less and the age at first startup for 45% of entrepreneurs was 30 years of age or more (The Wall Street Journal, March 19, 2012).
a. Suppose a sample of 200 entrepreneurs will be taken to learn about the most important qualities of entrepreneurs. Show the sampling of ṕ where ṕ is the sample proportion of entrepreneurs whose first startup was at 29 years of age or less.
b. What is the probability that the sample proportion in part (a) will be within ± .05 of its population proportion?
c. Suppose a sample of 200 entrepreneurs will be taken to learn about the most important qualities of entrepreneurs. Show the sampling of ṕ where ṕ is now the sample proportion of entrepreneurs whose first startup was at 30 years of age or more.
d. What is the probability that the sample proportion in part (c) will be within ±.05 of its population proportion?
e. Is the probability different in parts (b) and (d)? Why?
f. Answer part (b) for a sample of size 400. Is the probability smaller? Why?

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