A certain mathematician spends a lot of time at a particular bar (let us call it
ID: 3175021 • Letter: A
Question
A certain mathematician spends a lot of time at a particular bar (let us call it Farside). Over time he notices that whenever a glass of whiskey is ordered, the amount in the glass is approximately normally distributed with a mean of 5 oz. and a standard deviation of .25 oz.. I sit down next to my friend the mathematician and order a whiskey. (a) Calculate the probability that my glass of whiskey is greater than 5.5 oz. (b) What is the volume size of the glass that can contain 99 percent of all pours? (c) Assuming that each pour is independent, what is the probability that the next 3 glasses all contain more than 5.5 oz?Explanation / Answer
a)For x = 5.5oz, we find the z value , i.e z = (5.5 - 5) / 0.25 = 2
Hence P(x > 5.5) = P(z > 2) = [total area] - [area to the left of 2] from the Z table
= 1 - 0.9772 =0.0228
b) We find the Z value for ((percent or 0.99 proportion which is z= 2.576
z = (Glass size - Population mean)/ standard deviation
2.576 = (GS - 5)/0.25
Therefore GLASS SIZE which can contain 99 percent of all pours is 5.644
c) since they are independent events and as we already know the value of P(X>5.5) = 0.0228
the probability next three glasses are greater than 5.5oz is = P(X>5.5)* P(X>5.5)* P(X>5.5)
= 0.02283 = 0.00001185
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