1) [15 points]

Suppose that in Rochester there is a 2/3 chance for it to be cloudy on any given day.

a) [5 points] What is the average number of cloudy days in a typical year of 365 days? What is the standard deviation?

b) [5 points] How unlikely is it that in a given year there will be 225 cloudy days or less? (Hint: use the table of standard deviations for the normal distribution in the notes or the text)

c) [5 points] If there were only 200 cloudy days in the year, how surprised would you be? If there were 300 cloudy days in the year, how surprised would you be? What would be the range of cloudy days that would include 99% of all years?

2) [15 points]

Suppose there is an election between two candidates, A and B. It is estimated that the probability a voter will vote for A is 11/20, and the probability that a voter will vote for B is 9/20. Suppose that 100 people will vote in the election.

a) [5pts] What is the average number of votes that candidate A should expect to get? What is the standard deviation?

b) [5pts] What is the likely range of votes (to 99% certainty) that candidate A might expect to get?

c) [5pts] How likely is it that candidate B will win the election?