STA218 Assignment for the Midterm

Just a few extra questions

For the midterm text, you are responsible for the readings and questions from Quiz Assignments 1-5, and also for the exercises on this page. For more information about the midterm, click here.

The questions in this assignment can be answered based on Section 6.4: "The sampling distribution of a sample proportion." But the discussion in Section 6.4 depends upon Section 4.2 (The binomial probability distribution) and Section 5.4 (The mormal approximation to the binomial) -- both of which we skipped. So please refer to your lecture notes. You are responsible for the material in the blue box on page 206, if it is understood that by x/n, we mean x-bar based on a sample of zeros and ones.

  1. Suppose that the proportion of individuals in the population with a certain characteristic (for example, they purchased beer during the past 30 days) is denoted by p. We select a single individual at random from the population, letting X=1 if she has the characteristic, and X=0 if she does not.
    1. Give the probability ditribution of X.
    2. Calculate E(X)=µ. Show your work and circle your final answer.
    3. Calculate σ. Show your work and circle your final answer.
  2. Suppose that only 3% of computer owners have a Macintosh. We sample n=100 computer owners (randomly with replacement). Is this a big enough sample to use the normal distribution to make probability statements about the sample proportion of Mac owners? Answer YES or NO and show your work. My answer is NO, 0.03 ± 0.05117617.
  3. Do Exercises 6.24, 6.26, and 6.27 a and b. For b, give the shortest possible interval. For all threee questions, verify that the sample size is big enough. Also do Exercise 6.44.
  4. Suppose that on a corporate Web server, the probability that there will be no down time during a one day (24-hour) period is 0.95, and that having any down time or not on successive days are independent events. What is the probability of having no down time on 350 or more days during a one year (365 day) period?
    1. Is the sample size large enough so we can use the normal distribution? (YES, 0.95 ± 0.03422328)
    2. What is the probability? Give a number. (0.2177)

Do the assigned problems in preparation for the midterm. They are not to be handed in.