Among coffee drinkers men drink a mean of 3.2 cups per day with a standard devia

Question

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).

Explanation / Answer

Given X~Normal(mean=3.2, s=0.8) ------------------------------------------------------------------------------------------- a. what proportion drink 2 cups per day or more? P(X>=2) = P((x-mean)/s >= (2-3.2)/0.8) =P(Z>= -1.5) = 0.9332 (check standard normal table) ------------------------------------------------------------------------------------------- b. What proportion drink no more than 4 cups per day P(X c = 3.2 + 1.645*0.8 =4.516

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