15. Beanstalks In some cities, tall people who want to meet and socialize with other tall people can join Beanstalk Clubs. To qualify, a man must be over 6'2" tall, and a woman over 5'10". According to the National Health Survey, heights of adults may have a Normal model with mean heights of 69.1" for men and 64.0" for women. The respective standard deviations are 2.8" and 2.5".
a) You're probably not surprised to learn that men are generally taller than women, but what does the greater standard deviation for men's heights indicate?
b) Are men or women more likely to qualify for Beanstalk membership?
c) Beanstalk members believe that height is an important factor when people select their spouses. To investigate, we select at random a married man and, independently, a married woman. Define two random variables, and use them to express how many inches taller the man is than the woman.
d) What's the mean of this difference?
e) What's the standard deviation of this difference?
f) What's the probability that the man is taller than the woman (that the difference in heights is greater than 0)?
g) Suppose a survey of married couples reveals that 92% of the husbands were taller than their wives. Based on your answer to part f, do you believe that people's choice of spouses is independent of height? Explain.
7. Facebook According to Pew Research, 50% of adults and 75% of teenagers were using a social networking site in early 2012. Most of that activity was on Facebook.
Let's assume these probabilities apply strictly to Face- book (after all, MySpace is empty, right?) Among a group of 10 people, what's the probability that
a) at least one of the people was not on Facebook if they were all adults?
b) at least one of the people was not on Facebook if they were all teenagers?
c) at least one of the people was not on Facebook if half were teenagers?
The following non-text problem C3: During the 2013-2014 regular season, Brian Roberts of the Charlotte Hornets had a free-throw shooting percentage was 0.940.
a. What is the probability that the first free throw he manages to hit is on his fourth attempt?
b. On average, how many free throws will Roberts have to take before he makes one?
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