1. In a certain county in which people are selected to serve on a jury, the population is 35% African-American. Suppose over the course of a year a particular judge selects 394 jurors, of which 146 were African-American. Assume that the random variable, X=number of African-Americans, fits the assumptions for a Binomial random variabl

a. Calculate the mean number of African-Americans expected in 394 jurors. b. Calculate the standard deviation of African-Americans expected in 394 jurors. c. Using our rule of thumb for "unusual" or "significant values, what are the usual numbers of African-Americans expected in 394 jurors? Is the judge's 146 African-Americans an unusual number?

2) In a recent year, there were 333 murders in NY city. Let the random variable X be the number of murders occurring in one day.

a. Justify that this random variable has a Poisson distribution.

b. Estimate the mean number of murders per day (assume 365 days in the year) c. Find the probability that there will be no murders in a day in NY city. d. Find the probability that there will be at least one murder in a day in NY city.

3) The annual per capita consumption of ice cream (in pounds) in the United States can be approximated by normal distribution with a mean 20.7 lbs and a standard deviation of 4.2 pounds.What percent of the US population eats more than 26 lbs of ice cream a year?

a. What percent of the US population eats less than 15 lbs of ice cream a year? b. Find the 99^th percentile for annual ice cream consumption in the US. c. What percent of the US population eats between 15 lbs and 25 lbs of ice cream in a year? d. What is the probability that two randomly selected people from the US both eat less than 15lbs of ice cream a year? e. A randomly selected group of 16 people measure their ice cream consumption for a year. What is the probability that their mean ice cream consumption is more than 22 lbs per year? A randomly selected group of 16 people measure their ice cream consumption for a year. What is the probability that their mean ice cream consumption is more than 22 lbs per year?