A local financial advisor claims that only 20% of his investors lose money. In o

Question

A local financial advisor claims that only 20% of his investors lose money. In order to check out his claim, you sneak into his office during lunch and randomly mite down the names of 20 of his investors. You contact these 20 investors and ask them if they lost money. Since the number of investors who lose money is assumed to be a binomial random variable., calculate the following probabilities. P(4 investors lose money) = P(4 or fewer investors lose money) = P(more than 4 investors lose money) = If you actually found 9 investors who lost money in the sample of 20 investors, would you recommend that all your friends use this financial advisor? Explain and give reasons for your recommendation.

Explanation / Answer

This is an instance of binomial distribution. Thus, use the following formula.

P(X=r)nCr(p)^r(q)^n-r, where, p denotes the probability of event to occur, n i sthe total number of trials and r denotes number of events.

a.P(X=4)=20C4(0.20)^4(0.80)^16=0.2181

b. P(Xless than equal to 4)=P(X=0)+P(X=1)+P(X=2)+...+P(X=4)=0.6296

C. P(more than 4)=1-P(X less than equal to 4)=1-0.6296=0.3704

d. Probability of 9 investors who lost money is 9/20=0.45, which is (0.45-0.20)=0.25 that is 25% higher than the claim by the investor. So, advice is to avoid the investor.

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