Probability

Due: 10/23. This assignment is to be done by hand. Please show your work.

1. Lisa wants to conduct a survey about people's attitudes towards the death penalty. She posts a questionnaire on the internet asking people to respond to her survey. After one month, she collects her data and presents her results as a representation of people's attitudes towards the death penalty. Can Lisa's data be considered representative of the population? Be sure to provide a justification for your answer. What alternative selection method should Lisa use if she wants her data to be representative?

2. Does aspirin reduce the risk of a subsequent heart attack? Here are the data for subjects who had survived one heart attack and who then began to take a placebo or aspirin each day.

Attack / No Attack
Placebo / 239 / 10,795 / 11,034
Aspirin / 139 / 10,898 / 11,037
378 / 21,693 / 22,071

Using thisdata;calculate the probability of having a heart attack when 1) taking a placebo, and 2) taking aspirin.

3. The Internal Revenue Service needs to hire 150 claim reviewers. According to previous research, applicants who score at or above the 80th percentile on the PDQ mathematics test complete successfully the IRS training program and are then certified as claim reviewers. The PDQ mathematics has a mean of 50 and a standard deviation of 12. After the job announcement was advertised, 1637 people applied to take the test. Use this information to complete the following.

  1. How many of the people taking the test do you predict will achieve a score high enough to be considered for the job of claim reviewer?
  1. What score is necessary to be considered for this job?
  1. Thomas scores a 70 on the test. What is his percentile ranking?
  1. Of the applicants taking the test, how many do you estimate will
    1. have a score less than 45?
    2. have a score between 38 and 72?
    3. have a score greater than 72 or a score less than 38?
  1. What is the probability of randomly selecting 3 people whose score is 50 or greater?
  1. What is the probability of randomly selecting 3 people whose score is 65 or greater?

4. The table below shows the result of survey by a car dealer about the relationship between income level and type of car they buy. A total of 250 participants were randomly sampled.

  1. Calculate and explain the following:
  2. P(h1)
  1. P(D1)
  1. P(h1 ∩ D1)
  1. P(h1 U D1)
  1. P(h2 U D3)
  1. P(h1|D3)
  1. P(D1|h2)

5. Tests of deception typically work by asking a series of questions that represent honest behaviors that few people actually perform. These questions include “I always obey the speed limit when driving” or “I always tell people the truth, even when it may hurt their feelings”. According to a recent study, when given eight questions of this type and told to answer truthfully, the typical person will agree with three of these statements. Assuming that these data are valid, respond to the following questions.

  1. What is the proportion of questions that the typical person will say is true of them (i.e., p)?
  2. What is the proportion of questions that the typical person will say is not true of them (i.e., q)?
  3. Using these data, create a binomial distribution that describes potential outcomes.
  4. What are the probabilities of the following outcomes?
  5. X ≥ 4
  6. X > 5
  7. X ≤ 2
  8. X ≥ 6
  9. Assume your friend takes this test and earns a score of 7. Do you think your friend is answering honestly? Explain your answer.