# Question of probability

I just don't understand the way this question is solved. Can you please do it in a different way?  Thanks.

A shoe producer makes a variety of footwear, including indoor slippers, children's shoes, and flip-flops. To keep up with increasing
demand, it is considering three expansion plans: (1) a small factory with yearly costs of \$150,000 that will increase the production of flip-
flops to 400,000; (2) a: mid-sized factory with yearly costs of  \$250,000 that will increase the production of  flip-flops to 600,000; and (3)
a large factory with yearly costs of \$350,000 that will increase the production of flip-flops to 900,000. The profit per flip-flop is projected
to be \$0.75. The probability distribution of the increased demand for flip-flops is provided. Let x represent the amount of profit the
producer will make.

Complete parts a through c below.

Small Plan E(x)=       (Type an integer or a decimal.)
Mid-Sized Plan E(x) =   (Type an integer or a decimal.)
Large Plan E(x) =      (Type an integer or a decimal.)

b. Calculate the standard deviation for each of the expansion plans.

Small Plan Sigma(x) =     (Round to the nearest whole number as needed.)
Mid-Sized Plan Sigma(x) =   (Round to the nearest whole number as needed.)
Large Plan Sigma(x) =   (Round to the nearest whole number as needed.)

c. Which expansion plan would you suggest Provide the statistical reasoning behind your selection.
The (a.large, b.small, c.mid-size) plan has the largest expected profit. This plan has a much (a.higher, b.lower) standard deviation than the

other plans so this would be a good choice for those who can absorb (a.less, b.more)  risk than the other plans.

SOLUTION
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###### Who is Participating?

OwnerCommented:
Costs      Production      Proffit      Net Profit      BreakEven Units  break even as percentage of capacity
Small      150000      400000           300000      150000            200000                     50%
Medium      250000      600000         450000      200000           333333                      56%
Large      350000      900000        675000            325000          466667                        52%
Small and Large have break even units at about 50% capacity
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Author Commented:
This question is kind of hard for me. Can you please elaborate it.
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Commented:
The problem is impossible to solve with the data given.
1.What is p(x)?
2. There is no mention of standard deviation.

As you have recognized, the critical info is the probability of selling the product.
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Random thoughts:
It appears that the cheapest producing factory is 2
Build two 2 rather than one of any other
cost of operating factory not given (or needed for your problem)
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Author Commented:
I am sorry i miss some data.

Demand      Probability
350000      0.1
700000      0.4
900000      0.5
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Commented:
does it mean that the probability of a demand of 350000 is 1/10
and that the probability of a demand of 700000 is greater at 4/10?
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Author Commented:
Thanks.
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