2.Among coffee drinkers, men drink a mean of 3.2 cups per day with a standard de

Question

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.

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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