Iron Burr operates a booth which sells specialty merchandise at the State Fair. This year he is planning to sell t-shirts which are inscribed: THE STATE FAIR FOR EVERYONE The price of the t-shirts is $25.00 each. Mr Burr buys plain white t-shirts from a factory at a cost of $864 per gross (144 shirts), with a 3% discount for payment within 10 days, which he always takes. Mr Burr inscribes the design on the t-shirts, himself, and estimates that his labor is worth $4.00 per shirt. Unsold t-shirts are useless, but can be sold to a scrap dealer for $0.16 per pound; there are eight t-shirts in a pound. The number of t-shirts which will be sold at the State Fair is, of course, unknown. But, based on previous experience, Mr Burr estimates that the mean sales are 3 gross, and that the probability of selling more than 3 gross decreases as the quantity increases. Use the following cumulative distribution to determine number of gross of t-shirt that Mr Burr should prepare for the State Fair and the profits excluding Mr Burr's labor. X 1 3 4 5 6. 7 8 9. 10 P(x) 0.050 0.199 0.423 0.647 0.815 0.916 0.966 0.988 0.996 0.999 1.0

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Iron Burr operates a booth which sells specialty merchandise at the State Fair. This year he is
planning to sell t-shirts which are inscribed:
THE STATE FAIR
FOR EVERYONE
The price of the t-shirts is $25.00 each. Mr Burr buys plain white t-shirts from a factory at a
cost of $864 per gross (144 shirts), with a 3% discount for payment within 10 days, which he
always takes. Mr Burr inscribes the design on the t-shirts, himself, and estimates that his labor
is worth $4.00 per shirt. Unsold t-shirts are useless, but can be sold to a scrap dealer for $0.16
per pound; there are eight t-shirts in a pound. The number of t-shirts which will be sold at the
State Fair is, of course, unknown. But, based on previous experience, Mr Burr estimates that
the mean sales are 3 gross, and that the probability of selling more than 3 gross decreases as
the quantity increases. Use the following cumulative distribution to determine number of gross
of t-shirt that Mr Burr should prepare for the State Fair and the profits excluding Mr Burr's
labor.
0 1
P(x) 0.050 0.199 0.423 0.647 0.815 0.916 0.966 0.988 0.996 0.999 1.0
2
3
4
5
6 7
8
9
10
X
Transcribed Image Text:Iron Burr operates a booth which sells specialty merchandise at the State Fair. This year he is planning to sell t-shirts which are inscribed: THE STATE FAIR FOR EVERYONE The price of the t-shirts is $25.00 each. Mr Burr buys plain white t-shirts from a factory at a cost of $864 per gross (144 shirts), with a 3% discount for payment within 10 days, which he always takes. Mr Burr inscribes the design on the t-shirts, himself, and estimates that his labor is worth $4.00 per shirt. Unsold t-shirts are useless, but can be sold to a scrap dealer for $0.16 per pound; there are eight t-shirts in a pound. The number of t-shirts which will be sold at the State Fair is, of course, unknown. But, based on previous experience, Mr Burr estimates that the mean sales are 3 gross, and that the probability of selling more than 3 gross decreases as the quantity increases. Use the following cumulative distribution to determine number of gross of t-shirt that Mr Burr should prepare for the State Fair and the profits excluding Mr Burr's labor. 0 1 P(x) 0.050 0.199 0.423 0.647 0.815 0.916 0.966 0.988 0.996 0.999 1.0 2 3 4 5 6 7 8 9 10 X
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