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 cup per day or more? B) what proportion drink no more than 4cup per day? C) If the top 5% of coffee drinkers are considered heavy coffee drinkers what is the minimum number of cups per day consumed by a heavy coffee drinker? Hint: find the 95th percentile
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!
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
A) what proportion drink 2 cup per day or more?
B) what proportion drink no more than 4cup per day?
C) If the top 5% of coffee drinkers are considered heavy coffee drinkers what is the minimum number of cups per day consumed by a heavy coffee drinker? Hint: find the 95th percentile
Given Information : 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 .
Define random variable X denotes number of coffee drinks per day.
Here, X ~> Normal (μ=3.2, σ=0.8)
(a)
We need to compute . The corresponding z-value needed to be computed is :
Therefore, we get that
Proportion drink 2 cup per day or more = 93.32%
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