# Mathematics

1. Total cholesterol in children aged 10-15 is assumed to follow a normal distribution with a mean of 191 and a standard deviation of 22.4. a. What proportion of children 10-15 years of age have total cholesterol between 180 and 190? b. What proportion of children 10-15 years of age would be classified as hyperlipidemic (Assume that hyperlipidemia is defined as a total cholesterol level over 200)? c. What is the 90th percentile of cholesterol? 2. Among coffee drinkers, men drink a mean of 3.2 cups per day with a standard deviation of 0.8 cups. Assume the number of coffee drinks per day follows a normal distribution. a. What proportion drink 2 cups per day or more? b. What proportion drink no more than 4 cups per day? c. If the top 5% of coffee drinkers are considered heavy coffee drinkers, what is the minimum number of cups consumed by a heavy coffee drinker? Hint: Find the 95th percentile. 3. A study is conducted to assess the impact of caffeine consumption, smoking, alcohol consumption and physical activity on cardiovascular disease. Suppose that 40% of participants consume caffeine and smoke. If 8 participants are evaluated, what is the probability that: a. Exactly half of them consume caffeine and smoke? b. At most 6 consume caffeine and smoke? 4. A recent study of cardiovascular risk factors reported that 30% of adults met criteria for hypertension. If 15 adults are assessed, what is the probability that a. Exactly 5 meet the criteria for hypertension? b. None meet the criteria for hypertension? c. Less than or equal to 7 meet the criteria for hypertension? 5. Diastolic blood pressures are assumed to follow a normal distribution with a mean of 85 and a standard deviation of 12. a. What proportion of people have diastolic blood pressure less than 90? b. What proportion have diastolic blood pressures between 80 and 90? c. If someone has a diastolic blood pressure of 100, what percentile is he/she in? Chapter 6. 1. A study is run to estimate the mean total cholesterol level in children 2-6 years of age. A sample of 9 participants is selected and their total cholesterol levels are measured as follows. 185 225 240 196 175 180 194 147 223 Generate a 95% confidence interval for the true mean total cholesterol levels in adults with a history of hypertension. 2. A clinical trial is planned to compare an experimental medication designed to lower blood pressure to a placebo. Before starting the trial, a pilot study is conducted involving 10 participants. The objective of the study is to assess how systolic blood pressure changes over time untreated. Systolic blood pressures are measured at baseline and again 4 weeks later. Compute a 95% confidence interval for the difference in blood pressures over 4 weeks.