1. Suppose we want to estimate the mean BMI for women in pregnancy at 20 weeks gestation. If we have a sample of 100 women and measure their BMI at 20 weeks gestation, what is the probability that the sample mean is within 1 unit of the true BMI if the standard deviation in BMI is taken to be 3.6?

2. An experimental drug has been shown to be 75% effective in eliminating symptoms of allergies in animal studies. A small human study involving 6 participants is conducted. What is the probability that the drug is effective on more than half of the participants?

3. In a study of women and preterm delivery, suppose BMI at 16 weeks gestation has a mean 28.5 with a standard deviation of 3.6 and BMI is assumed to follow a normal distribution. Find thefollowing:

a. The proportion of women with BMI> 30.

b. The proportion of women with BMI>40.

c. The BMI that separates the top 10% from the rest.

4. A study is conducted to compare an experimental medication for migraine headaches to a currently available medication. A total of 50 patients are enrolled in the study and each patientreceives both treatments. Each participant is asked if the assigned medication causes anystomach upset. Among the 50 participants, 12 report stomach upset with the experimentalmedication. Construct a 90% confidence interval for the proportion of participants who might experience stomach upset with the experimental medication.

5) A 95% confidence interval for the mean diastolic blood pressure in women is 62 to 110. What isthe margin of error?

6. Recent recommendations suggest 60 minutes of physical activity per day. A sample of 50 adultsin a study of cardiovascular risk factors report exercising a mean of 38 minutes per day with astandard deviation of 19 minutes. Based on the sample data, is the physical activity significantlyless than recommended? Run the appropriate test at a 1% level of significance