Answer in Excel, 1. Total Cholesterol in children aged 10-15 years is as 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 a total cholesterol between 180 and 190? b. What proportion of children 10-15 years of age would be clasified as hyperlipidemic (Assume that hyperlipidmia is defined as a total cholesteroal level over 200)? c. What is the 90th percentile of cholesterol levels? 2. Amoung coffee drinkers, men drink a mean of 3.2 cups per day, with a standard deviation of 0.8 cup. Assume a. If the top 5% of coffee drinkers are considered heavy coffee drinkers, what is the minimum number of cups per day consumed by heavy coffee drinkers? Hint: Find the 95th percnetile. 3. A study is conducted to assess the impact of coffeine 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 hypertention. If 15 adults are assessed, what is the probability that: a. Exactly 5 meet the crateria for hypertention? b. None meet the criteria for hypertention? c. Less than or equal to 7 meet the crateria for hypertention? 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. Whatproportion of people have diastolic blood pressure between 80 and 90? c. If someone has a diastolic blood pressure of 100, what percentile is he/she in?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Answer in Excel,
1. Total Cholesterol in children aged 10-15 years is as assumed to follow a
a. What proportion of children 10-15 years of age have a total cholesterol between 180 and 190?
b. What proportion of children 10-15 years of age would be clasified as hyperlipidemic (Assume that hyperlipidmia is defined as a total cholesteroal level over 200)?
c. What is the 90th percentile of cholesterol levels?
2. Amoung coffee drinkers, men drink a mean of 3.2 cups per day, with a standard deviation of 0.8 cup. Assume
a. If the top 5% of coffee drinkers are considered heavy coffee drinkers, what is the minimum number of cups per day consumed by heavy coffee drinkers? Hint: Find the 95th percnetile.
3. A study is conducted to assess the impact of coffeine 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
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 hypertention. If 15 adults are assessed, what is the probability that:
a. Exactly 5 meet the crateria for hypertention?
b. None meet the criteria for hypertention?
c. Less than or equal to 7 meet the crateria for hypertention?
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. Whatproportion of people have diastolic blood pressure between 80 and 90?
c. If someone has a diastolic blood pressure of 100, what percentile is he/she in?
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