The amount of caffeine in a cup of coffee varies considerably, even if it is bre

Question

The amount of caffeine in a cup of coffee varies considerably, even if it is brewed by the same person using the same brewing method and ingredients. Suppose the amount of caffeine in a 5 oz cup of coffee created using the Drip-method is approximately normally distrubuted with mean 130 mg and standard deviation 20 mg. An article claimed that 6.35% of 5 oz coffees had enough caffeine to make the heart race. For this mean and standard deviation, what is the value of the caffeine (in mg) that would make the heart race?

Explanation / Answer

The amount of caffeine in a cup of coffee varies considerably, even if it is brewed by the same person using the same brewing method and ingredients. Suppose the amount of caffeine in a 5 oz cup of coffee created using the Drip-method is approximately normally distrubuted with mean 130 mg and standard deviation 20 mg. An article claimed that 6.35% of 5 oz coffees had enough caffeine to make the heart race. For this mean and standard deviation, what is the value of the caffeine (in mg) that would make the heart race?

Z value for top 6.35% =1.526 ( from standard normal distribution)

X=mean+z*sd = 130+1.526*20

=160.52

The required value of the caffeine = 160.52 mg

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