Complete AND attach homework (Chapter Review) problems:

• #1 on page 237 (10 points): __________________
• # 2 on page 237 (10 points): _________________
• # 4 on page 238 (10 points): _________________

Attach and show all work for the problems below.

Problem 1 (20 Points): In 2009, a suburb in Denver experienced 3,789 auto thefts while having 83,375 cars. Assuming the population of cars for 2010 is about the same in this suburb, calculate:

• the probability of having your car stolen: never, 1 time, 2 times, and more than 3 times during 2010 in this suburb.

• The mean and standard deviation of this distribution

• Create a bar graph (pdf) for this distribution below.
• Create a line graph (cdf) for this distribution below (place both PDF and CDF on the same graph.)

Problem 2 (20 points): A genetics experiment shows a specific gene expresses itself (i.e., phenotype - observable characteristic or trait) in an organism in more than one way or location on the organism. Let the way the gene expresses itself be the random variable x. The number of ways and their associated probabilities for this gene phenotype is shown in the table to the right.

Complete / compute the following:

• Make the table represent a valid discrete distribution by calculating the value of gene expression 2 (shown by the ?).
• Calculate the distribution's m and s.
• Plot the probability density function (PDF) as a bar graph AND the cumulative distribution curve (CDF) as a line graph in the chart below.

• Calculate the probability of this gene expressing itself more than twice.
• Compute the maximum usual value for this distribution using the Range of Thumb Rule.
• When could it be said an unusually high number of gene expressions had occurred?
• Why would asking the question: "What is the probability of this gene expressing itself 3.3 time in this organism?" be inappropriate?

Problem 3 (20 points): Fremont county has 12% of persons from Italian descent. In jury trials involving 12 jury members, calculate the probability that:

• exactly 5 of the jurors will be of Italian descent.
• less than 3 of the jurors will be of Italian descent.

Plot p(x) [probability density function] on the graph below in bar graph form (only go up to 10 jurors).

Problem 4 (10 points): A classic example of the Poisson distribution involves the number of deaths caused by horse kicks to men in the Prussian Army between 1875 and 1894. Data for 14 corps (a corps is a military unit of about 6,000 mounted men) were combined for the 20-year period and the 280 corps-years included a total of 196 deaths. After finding the mean number of deaths per corps-year, find the probability that a randomly selected corps-year has the following number of deaths:

• 0 deaths
• 1 death
• more than 2 deaths