The Wall Street Journal reported that 37% of all entrepreneurs who opened new U.S. businesses in the

Question:

The Wall Street Journal reported that 37% of all entrepreneurs who opened new U.S. businesses in the previous year were female (The Wall Street Journal, May 13, 2015).
a. Suppose a random sample of 300 entrepreneurs who opened new U.S. businesses in the previous year will be taken to learn about which industries are most appealing to entrepreneurs. Show the sampling of p, where p is the sample proportion of entrepreneurs who opened new U.S. businesses in the previous year that are female.
b. What is the probability that the sample proportion in part (a) will be within 6.05 of its population proportion?
c. Suppose a random sample of 30,000 entrepreneurs who opened new U.S. businesses in the previous year will be taken to learn about which industries are most appealing to entrepreneurs. Show the sampling of p where p is the sample proportion of entrepreneurs who opened new U.S. businesses last year that are female.
d. What is the probability that the sample proportion in part (c) will be within 6.05 of its population proportion?
e. Is the probability different in parts (b) and (d)? Why?
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