An investment company claims that only 10% of their portfolios give a negative return on investment in a 1-year span. You take a random sample of 150 of their portfolios and find that 20 had a negative 1-year return:
a) Show that the number of portfolios that have a negative 1-year return follow a binomial distribution.
b) Find the probability that at least 20 portfolios have a negative 1-year return using a normal approximation.
c) Your team has decided that if P(X ≥ 20) is lower than 0.01, then the investment company’s claim that only 10% of their portfolios give a negative return to investment in a 1-year span should be rejected. What should your team decide based on the probability found in 7.39b? Explain.