Please see the attached file for full problem description.
According to Census Bureau, deaths in the United States occur at a rate of 2,425,000 per year. The National Center for Health Statistics reported that the three leading causes of death during 1997 were heart disease (725,790), cancer (537,390), and stroke (159,877). Let H,C, and S represent the events that a person dies of heart disease, cancer and stroke, respectively.
a. Use the data to estimate P(H), P(C), and P(S).
b. Are events H and C mutually exclusive? Find P(HC).
c. What is the probability that a person dies from heart disease or cancer?
d. What is the probability that a person dies from cancer or a stroke?
e. Find the probability that someone dies from a cause other than one of these three
In a survey of MBA students, the following data were obtained on "students' first reason for application to the school in which they matriculated."
Reason for Application
Quality Convenience Other Totals
Full Time 421 393 76 890
Part Time 400 593 46 1039
Totals 821 986 122 1929
a. Develop a joint probability table for these data.
b. Use the marginal probabilities of school quality, cost/convenience, and other to comment on the most important reason for choosing a school.
c. If a student goes full time, what is the probability that school quality is the first reason for choosing a school?
d. If a student goes part time, what is the probability that school quality is the first reason for choosing a school?
e. Let A denote the event that a student is full time and let B denote the event that the student lists school quality as the first reason for applying. Are events A and B independent? Justify your answer.
A study of job satisfaction was conducted for four occupations: cabinetmaker, lawyer, physical therapist, and system analyst. Job satisfaction was measured on a scale of 0-100. The data obtained are summarized in the following crosstabulation.
Occupation Under 50 50-59 60-69 70-79 80-89
Cabinetmaker 0 2 4 3 1
Lawyer 6 2 1 1 0
Physical Therapist 0 5 2 1 2
System Analyst 2 1 4 3 0
a. Develop a joint probability table.
b. What is the probability one of the participants studied had a satisfaction score in the 80s?
c. What is the probability of a satisfaction score in the 80s given the study participant was a physical therapist?
d. What is the probability one of the participants studied was a lawyer?
e. What is the probability one of the participants was a lawyer and received a score under 50?
f. What is the probability of a satisfaction score under 50 given a person is a lawyer?
g. What is the probability of a satisfaction score of 70 or higher?
The following is based on Census Bureau data and shows how to calculate probabilities, determine exclusivity, and create a probability table.