How would I answer B and C? Answers to the following questions should be calcula

Question

How would I answer B and C?

Answers to the following questions should be calculated in Matlab and given to 4 decimal places. Be careful not to introduce errors by rounding in any intermediate calculations as this may lead to an incorrect final answer In a certain workshop, the total cost, C for servicing a car is where X is the cost of parts and Y is the time (in hours) taken to perform the service. Suppose, for a randomly chosen car, that x N (130, 22) and YN (2.5,0.64) independently. (a) Find E(C) 330 (b) Find var(C) (C) Find the probabllity that the total cost of service, for a randomly chosen car, will be no more than $350.00

Explanation / Answer

Answer to the parts with all calculations:

a. E(C)

= E(X+80Y)

= E(X) + E(80Y)

= E(X) + 80E(Y)

= 130+80*2.5

= 330

b.

Var(C)

= Var(X+80Y)

= Var(X) + 80^2E(Y)

= (22^2) + (80^2) * (.6^2)

= 2788

c.

P(C<350)

= P(Z< (350-E(C))/STDEV(C) )

= P(Z< (350-330)/sqrt(2788))

=P(Z<(350-330)/SQRT(2788))

=P(Z<0.379)

=0.6475

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