Statistics 101-An investment advisor claims that 60 percent of the stocks she recommends beat the market

Subject: Mathematics    / Statistics
Question

4.25 An investment advisor claims that 60 percent of the stocks she recommends beat the market. To back up her claim, she recommends n stocks for the coming year. In fact, each of her recommendations has a 50 percent probability of beating the market and a 50 percent probability of doing worse than the market. Assuming independence, is she more likely to have at least a 60 percent success rate if she recommends 10 stocks or 100 stocks?

4.26 A woman wrote to Dear Abby, saying that she had been pregnant for 310 days
before giving birth [24]. Completed pregnancies are normally distributed with a
mean of 266 days and a standard deviation of 16 days. What is the probability
that a completed pregnancy lasts at least 310 days?

4.27 Explain why this is misleading:
In 70 percent of all traffic accidents, the driver is less than 10 miles from home.
These data show that drivers who are close to home feel safe and tend to relax
and pay less attention when they are, in fact, most likely to have an accident.

4.29 Explaining why he was driving to a judicial conference in South Dakota, the chief
justice of the West Virginia State Supreme Court said “I’ve flown a lot in my life.
I’ve used my statistical miles. I don’t fly except when there is no viable
132 ESSENTIAL STATISTICS, REGRESSION, AND ECONOMETRICS
alternative” [25]. What do you suppose the phrase used my statistical miles
means? Explain why you either agree or disagree with the judge’s reasoning.