Suppose that weekly gasoline sales at a corner Shell servicestation (in thousand

Question

Suppose that weekly gasoline sales at a corner Shell servicestation (in thousands of gallons) are approximately normallydistributed with a mean of 6 and a standard deviation of 1.3. Findthe probability that in a randomly chosen week the station willsell in excess of 4000 gallons of gasoline. How large of a storagetank should the station install if they receive weekly deliveriesof gasoline and wish to keep the probability of running out ofgasoline over the course of the week, down to 0.01 or less?

Explanation / Answer

We have given =6(in thousands of gallons), =1.3(inthousands of gallons). To find the probability that in a randomly chosen week thestation will sell in excess of 4000 gallons of gasoline. When X = 4( in thousands of gallons) Then the Z-score is given by, Z = X-/ =4-6/1.3 =-1.54. P(X>4)=1-P(X<=4) =1-P(Z<=-1.54) =1-0.061968 =0.938032. P(X<=x) = 0.01 =P(Z<=x-/)=0.01 =P(Z<=x-6/1.3)=0.01 =x-6/1.3=2.326 =x-6=3.0238 =x=3.0238+6 =9.0238. It is approximately 9( in thousands) of gallons of gasolinethat is to be stored.

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