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Data analysis with Census Bureau data.

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Ex 29
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

#33.
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
School Cost
School Or
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.

Ex 36

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.

Satisfaction Score
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?

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Solution Summary

The following is based on Census Bureau data and shows how to calculate probabilities, determine exclusivity, and create a probability table.

Solution provided by:
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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