The daily demand for substitute teachers in the Los Angeles school system follow

Question

The daily demand for substitute teachers in the Los Angeles school system follows the distribution given in the table. Los Angeles wants to know how many teachers to keep in the substitute teacher pool. Whether or not the substitute teacher is needed, it costs $30 per day to keep a sub in the pool. If not enough subs are available (from the pool) on a given day, subs from the neighboring system have to be used, at a cost of $54 per sub per day. How many teachers should Los Angeles have in the substitute teacher pool?

Number needed Probability

200 3%

500 30%

275 3%

550 6%

350 3%

600 7%

400 5%

650 3%

450 40%   

Explanation / Answer

given

data with Probability

Number needed Probability

200 3%

500 30%

275 3%

550 6%

350 3%

600 7%

400 5%

650 3%

450 40%

so On average Requirement of substitute teachers

E(X) =sum of x*P(X=x)

=200*0.03+500*0.3+275*0.03+550*0.06+350*0.03+600*0.07+400*0.05+650*0.03+450*0.04

=307.25

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