The Chartered Financial Analyst (CFA) Institute reported that 49% of its U.S. members indicate that lack of ethical culture within financial firms has contributed the most to the lack of trust in the financial industry. (Source: "Global Market Sentiment Survey 2014," cfa.is/Psk5O3.) Suppose that you select a sample of 100 CFA members.
a. What is the probability that the sample percentage indicating that lack of ethical culture within financial firms has contributed the most to the lack of trust in the financial industry will be between 48% and 53%?
b. The probability is 90% that the sample percentage will be contained within what symmetrical limits of the population percentage?
c. The probability is 95% that the sample percentage will be contained within what symmetrical limits of the population percentage?
d. Suppose you selected a sample of 400 CFA members. How does this change your answers in (a) through (c)? Given a normal distribution with µ = 100 and σ = 10, if you select a sample of n = 25, what is the probability that X is
d. There is a 65% chance that X is above what value?