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1) If x has a binomial distribution with p = .5, will the shape of the probability distribution be symmetric, skewed to the left, or skewed to the right? Explain why.
2) A meteorologist in Chicago recorded the number of days of rain during a 30 day period. If the random variable x is defined as the number of days of rain, does x have a binomial distribution? If not, why not? If so, are both values of n and p known?
3) If a person is given the choice of an integer from 0 to 9, is it more likely that he or she will choose an integer near the middle of the sequence than one at either end?
a) If the integers are equally likely to be chosen, find the probability distribution for x, the number chosen.
b) What is the probability that a person will choose a 4, 5, or 6?
c) What is the probability will not choose a 4, 5, or 6?
4) California residents love to complain about smog, freeway traffic, crime, and earthquakes, and although the quality of life in California may not be what it once was, roughly 75% of Californians think that it is "one of the best places to live" or "nice, but not outstanding". Suppose that five randomly selected California residents are interviewed.
a) Find the probability that all five residents think that California is a nice or very nice place to live.
b) What is the probability that at least one resident does not think that California is a nice or very nice place to live?
c) What is the probability that exactly one resident does not think that California is a nice or very nice place to live?
This solution finds probabilities from binomial distributions and discrete uniform distributions.