# SOLUTION: I need help with word problems, thank you! The caffeine content of a cup of home-brewed coffee is a normally distributed random variable with a mean of 115 mg with a standard de

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 Question 251866: I need help with word problems, thank you! The caffeine content of a cup of home-brewed coffee is a normally distributed random variable with a mean of 115 mg with a standard deviation of 20 mg. (a) What is the probability that a randomly chosen cup of home-brewed coffee will have more than 130 mg of caffeine? (b) Less than 100 mg? (c) A very strong cup of tea has a caffeine content of 91 mg. What is the probability that a cup of coffee will have less caffeine than a very strong cup of tea? (Data are from Popular Science 254, no. 5 [May 1999], p. 95.)Answer by stanbon(57940)   (Show Source): You can put this solution on YOUR website!The caffeine content of a cup of home-brewed coffee is a normally distributed random variable with a mean of 115 mg with a standard deviation of 20 mg. (a) What is the probability that a randomly chosen cup of home-brewed coffee will have more than 130 mg of caffeine? Find the z-value of 130 Then P(x > 130) = P(z > that z-value) ============================================= (b) Less than 100 mg? Find the z-value of 100. Then P(x<100) = P(z< that z-value) ============================================= (c) A very strong cup of tea has a caffeine content of 91 mg. What is the probability that a cup of coffee will have less caffeine than a very strong cup of tea? Find the z-value that corresponds to 91 mg using x = z*sigma + u 91 = z*20+115 z = -1.2 - Find P(z < -1.2) ======================== Cheers, Stan H. ---