Assignment Problems

Section 3.3

1. Are the events mutually exclusive (Yes or No)?
   Event A: Randomly select a person between 18 and 24 years old.
   Event B: Randomly select a person that drives a convertible.
2. Are the events mutually exclusive (Yes or No)?
   Event A: Randomly select a person who uses email.
   Event B: Randomly select a person that uses social networking.
   Problems 3-7. Use the table below to answer the questions.
   Nursing Majors. The table below shows the number of male and female students enrolled in nursing at a university for a recent semester. Find the specified probability.
   
3. The student is male or a non-nursing major.
4. The student is female or a nursing major.
5. A student is not male or a nursing major.
6. The student is male or a nursing major.
7. Are the events "being male" and "being a nursing major" mutually exclusive?
   Section 3.4
8. Perform the indicated calculation. ₂₄ P ₅
9. Experimental Group In order to conduct an experiment, 9 subjects are randomly selected from a group of 25 subjects. How many different groups of nine subjects are possible?
   Problems 10-11. Use the information below to answer the questions.
   Lock Combination. A combination lock has 5 programmable digits. The first digit may be set to whole number values from 1 to 5. The last four digits may be set to whole number values from 0-9.
10. How many lock combinations are possible if there are no restrictions?
11. What is the probability of selecting a combination code at random that ends with an odd number?
    Section 4.1
12. Determine if the random variable x is discrete or continuous. Explain the reason for your answer. x is the time required for workers at a factory to complete a task.
    Problems 13-17. Use the frequency distribution below to answer the questions.
    Extracurricular Activities. The number of school-related extracurricular activities per student.
    
    Activities 0 1 2 3 4 5 6 7
    Students 24 33 46 57 63 36 20 14
13. Use the frequency distribution to construct a probability distribution.
14. What is the mean of the probability distribution?
15. What is the variance of the probability distribution?
16. What is the standard deviation of the probability distribution?
17. Interpret the results in the context of the real-life situation. (For help with the interpretation, refer to similar worked examples in section 4.1.)
    Section 4.2
    Identifying binomial experiments. Use the information below to answer question 18.
    Lottery A state lottery randomly chooses 6 balls numbered 1 from 1 to 40. You choose 6 numbers and purchase a lottery ticket. The random variable represents the number of matches on your ticket to the numbers drawn in the lottery.
18. Is this experiment a binomial experiment? Explain your answer.
    Use the characteristics of the binomial distribution given below to answer questions 19- 21
    Suppose there is a binomial distribution with: n = 63 and p = 0.38
19. What is the mean of the binomial distribution?
20. What is the variance of the binomial distribution?
21. What is the standard deviation of the binomial distribution?
    Problems 22-25. Use the characteristics of the binomial experiment below to answer the questions.
    Travel Plans. Seventeen percent of married couples say they are planning a trip to Europe.
    You randomly select 15 married couples and ask each if they are planning to travel to Europe.
22. What is the probability that exactly 1 couple says they plan to travel to Europe?
23. What is the probability that more than 1 couple say they plan to travel to Europe?
24. What is the probability that at most 2 couples say they plan to travel to Europe?
25. What is the probability that less than 5 couples say they plan to travel to Europe?

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