# statistics

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A rocket fuel is to contain percent X of a particular chemical. The specification limits for X are 30 to 35%. The manufacturer will make a profit Q(x) on fuel per gallon as follows.

Q(x)=
10 cents if 30<=x<=35
5 cents if 35<x<40 or 25<x<30
-10 cents otherwise

Assuming X has a normal distribution with mean 33 and standard deviation 3, calculate expected profit, E(Q(X)).

I don't understand how to determine E(Q(X)) without a pdf.

• statistics -

n=100, p=1/4

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