Attach homework (Chapter Review) problems:
#1 on page 237 (10 points):
a) Valid PDF since the CDF = 1.00
d) Prob of getting at least 5 correct (meaning 5, 6, 7, 8, 9, or 10 correct.
What Meaning does the CDF have here?
Does it have ANY sensical meaning in the real world?
e) Since E = μ (see bottom of page 208)
f) Prob of getting at least one correct
g) No because probability tells you that you have a 89% probability of getting one correct answer just by guessing. So what. To just to pass you must get 70% and P(7) = 0.001 = 1:1000
# 2 on page 237 (10 points):
Use binomial distribution since it's applicable:
a) Expected number of sets tuned to Cold Case:
d) Exactly 3 tuned to Cold Case:
e) Unusual if NO sets tuned to Cold Case? NO since p(0) > 0,05
Just for kicks graphing the PDF and CDF:
# 4 on page 238 (10 points):
Use the Poisson Distribution since it's applicable:
a) Mean number of deaths each day:
b) Prob of 0 deaths on any given day:
c) Prob of 1 death on any given day:
d) Prob of more than 1 death on any given day:
e) NO contingency plan is needed for MORE than 1 death per day since it's so rare (0.02%):
Graphing the PDF and CDF over:
using equivalent Mathcad functions:
Attach and show all work for the problems below.
Problem 1 (20 Points): In 2009, a suburb in Denver experienced 2,789 auto thefts while having 43,375 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 3 times during 2010 in this suburb.
- The mean and standard deviation of this distribution
- Create a bar graph (pdf) for this distribution below.
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. The number of ways and their associated probabilities for this gene phenotype is shown in the table to the right.
Complete / compute the following:
- Confirm this table represents a valid discrete distribution
- Calculate the distribution's m and s.
- Plot the cumulative distribution curve (CDF) for this probability density function in the sketch 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?
Unusually High applies to x = 4 or 5 since the CDF is below 95% at x = 3 but above 95% at x = 4
Since this is a discrete distribution, asking about a gene expressing itself 3.3 times is non-sensical.
Problem 3 (20 points): Fremont county has 22% of persons from Italian descent. In jury trials involving 12 jury members, calculate the probability that:
- exactly 5 of the juniors 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).
Probability exactly 5 will be of Italian descent
Probability less than 3 (0, 1, 0r 2) will be of Italian descent
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
