Question

Bubba runs a barbeque stand that he sets up outside the Cardinal football stadium on the day of home football games. His specialty is smoked turkey legs and he has to smoke them the day before the game so they will be ready to sell on game day. He does not want to have too many prepared because if he does not sell them they will go to waste. On the other hand he makes about a 50% profit on each one he sells so he wants to have enough to meet demand. Figuring out just how many to make presents a tough problem for Bubba. Fortunately, Bubba keeps good sales records. He calculated that his sales of smoked turkey legs for all the many games he has worked averages 122 and has a standard deviation of 23. After thinking it through Bubba decides that he should stock enough turkey legs so that he has a 75% chance of having enough to meet demand on any given game day. How many smoked turkey legs should he make?(a)

If Bubba prepares 100 turkey legs what’s the chance that he will run short on any given game day?(b)

On what percentage of game days will Bubba’s demand for turkey legs be less than 135?(c)

Answer 1

Given:
Average sales of smoked turkey legs=μ=122
Standard deviation of smoked turkey legs = 23

Assuming that they are normally distributed
Number of smoked turkey legs for enough chance to meet 75% demand
P ( x < a ) = 0.75
Where a = required smoked turkey legs
P ((x-μ)/σ <   (a- μ)/σ ) = 0.75
P ( Z <   (a- μ)/σ ) = 0.75
From normal probability table
a-122/23= 0.675
a = 137.525
approximately a = 138
Hence , Bubba should prepare 138 smoked turkey legs so that he has a 75% chance to meet demand

a ) P ( x < 100 ) = P ((x-μ)/σ <   (100- 122)/23 )
                           = P (Z < -0.96 )
                           = 0.1685
If Bubba prepares 100 turkey legs then there will be 16.85 % chance he will run short on any game day.
b) P ( x < 135 ) == P ((x-μ)/σ <   (135- 122)/23 )
                           = P (Z < 0.57 )
                           = 0.7157
Thus 71.57% of game day will be Bubba’s demand for turkey legs be less than 135.