Assignment 3 – Due 10/18/15
1. Find the probability that when a couple has 3 children, they will have exactly 2 boys. Assume that boys and girls are equally likely and that the gender of any child is not influenced by the gender of any other child. Hint: Make a table of all possible outcomes to help you to visualize the events.
2. In a clinical trial of Lipitor, a common drug used to lower cholesterol, one group of patients was given a treatment of 10 mg atorvastatin tablets. (Lipitor consists of atorvastatin calcium). That group consists of 19 patients who experienced flu symptoms and 844 patients who did not. Estimate the probability that a patient taking the drug will experience flu symptoms.
3. Refer to the following table to answer this question. Assuming that 1 person is randomly selected from the 99 people included in the study, find the probability of selecting a subject who is pregnant or had a positive test result.
Pregnancy Test Results
Positive Test Result
(Pregnancy is Indicated) Negative Test Result
(Pregnancy is not Indicated)
Subject is Pregnant 80 5
Subject is not Pregnant 3 11
4. Mendel’s famous hybridization experiments involved peas. If two of the peas included in the following table are randomly selected without replacement, find the probability that the first selection has a green pod and the second selection has a yellow pod.
Peas Used in Hybridization Experiments
Pod Green 5 3
Yellow 4 2
5. A recent study reported that the prevalence of obesity is 45% in children ages 6-12. If 15 children are analyzed, what is the probability that 7 are obese?
6. Total cholesterol in children aged 10-15 is assumed to follow a normal distribution with a mean of 200 and a standard deviation of 27.5.
a. What proportion of children 10-15 years of age have a total cholesterol between 180 and 190?
b. If a sample of 20 children are selected, what is the probability that the mean cholesterol level will exceed 210?
7. Investigators want to assess the accuracy of self-reported smoking status. Participants are asked whether they currently smoke or not. In addition, laboratory tests are performed on hair samples to determine the presence or absence of nicotine. The laboratory assessment is considered the truth about nicotine. Use the data in the following table to answer the questions. Hint: Be careful of how the cells are arranged
Nicotine Absent Nicotine Present
Self-Reported Non-Smoker 82 32
Self-Reported Smoker 3 97
a. What is the sensitivity of self-reported smoking status?
b. What is the specificity of self-reported smoking status?
c. What is the positive predictive value of the laboratory assessment?
d. What is the negative predictive value of the laboratory assessment?