5. (4 points) BostonBrewing Company (makers of Samuel Adams beer) engages in str

Question

5. (4 points) BostonBrewing Company (makers of Samuel Adams beer) engages in strictquality control
measures. It is important to the brewers that their beer be storedat its proper temperature before
it is sold. The ideal temperature for storing (most of) their beersis 49 degrees F. The brewers drive
around to different distributors testing the storage temperatures.Suppose that storage temperatures
are normally distributed with mean 49 degrees F and standarddeviation 2 degrees. If a distributer
is found storing the beer at a temperature greater than 53.5degrees or less than 42 degrees then that
distributer has its permit to sell the beer revoked by thebrewers.
(a) What is the probability that a random distributer stores thebeer at a temperature less than 47.4
degrees?
(b) What is the probability that a random distributer stores thebeer at a temperature greater than
53.5 degrees?
(c) Is it possible, without doing the detailed calculations, todeduce which of the answers to the
previous two questions will be larger? If so, how?
(d) What is the probability that a random distributer does not loseits permit to sell the beer?
(e) If 6 stores are chosen at random, what is the probability that2 or fewer of them lose their
permits to sell the beer?

6. (3 points) NCT 7th 5.97 / NCT 6th 6.95 but change the part in(b) about the correlation being +0.6
to +0.5.
5. (4 points) BostonBrewing Company (makers of Samuel Adams beer) engages in strictquality control
measures. It is important to the brewers that their beer be storedat its proper temperature before
it is sold. The ideal temperature for storing (most of) their beersis 49 degrees F. The brewers drive
around to different distributors testing the storage temperatures.Suppose that storage temperatures
are normally distributed with mean 49 degrees F and standarddeviation 2 degrees. If a distributer
is found storing the beer at a temperature greater than 53.5degrees or less than 42 degrees then that
distributer has its permit to sell the beer revoked by thebrewers.
(a) What is the probability that a random distributer stores thebeer at a temperature less than 47.4
degrees?
(b) What is the probability that a random distributer stores thebeer at a temperature greater than
53.5 degrees?
(c) Is it possible, without doing the detailed calculations, todeduce which of the answers to the
previous two questions will be larger? If so, how?
(d) What is the probability that a random distributer does not loseits permit to sell the beer?
(e) If 6 stores are chosen at random, what is the probability that2 or fewer of them lose their
permits to sell the beer?

6. (3 points) NCT 7th 5.97 / NCT 6th 6.95 but change the part in(b) about the correlation being +0.6
to +0.5.

Explanation / Answer

Given X~Normal(=49, =2) (a) P(X

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