How much caffeine is in a cup of coffee? Suppose the amount, a, of caffeine in a cup of coffee A is normally distributed with mean 104 mg and standard deviation 12 mg, the amount, b, of caffeine in a cup of coffee B is normally distributed with mean 135 mg and standard deviation 9mg , and the amount, c, of caffeine in a cup of coffee C is normally distributed with mean 168mg and standard deviation 18 mg. Suppose we make a triple cup of coffee by mixing a cup of coffee A, a cup of coffee B, and a cup of coffee C together. Let X = total amount of caffeine in the triple cup. X = a + b + c. Let W = weighted caffeine taste in the triple cup, defined by W = 3a - 2b + c. Note: a,b, and c are
How much caffeine is in a cup of coffee? Suppose the amount, a, of caffeine in a cup of coffee A is
a) Calculate the
b) Calculate the standard deviation of X.
c) Calculate the expected value of W.
d) Calculate the variance of W.
e) If we pick a value k such that the probability that X > k equals .10 then calculate k?
f) The triple cup is considered bitter if X > 450. What is the probability the triple cup is bitter?
g) What is the probability that X is within two standard deviations of its expected value?
h) What is the probability that a is greater than b?
i) What is the probability that a, b, and c are all less than their 60th percentiles?
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