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

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 cups per day follows a normal distribution. a. What distribution drinks 2 cups per day per more? b. What proportion drinks no more than 4 cups per days? 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? d. If a sample of 20 men is selected, what is the probability that the mean number of cups per day is greater than 3?

Explanation / Answer

a) Z = (2-3.2)/0.8=-1.5

P(z>-1.5) = 1-0.066807=0.933

b)Z=(4-3.2)/0.8=1

P(z<1)=1-0.158 =0.842 from normal tables

c) Z for probabiltiy of 0.95 is 1.645

x = 3.2+ 1.645*0.8= 4.516 cups/day

d) Z= (3-3.2)/[0.8/sqrt(20)]=-1.118

P(z>-1.118)=1-0.131783=0.8682

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