13. After an electrical circuit component operates, there is some electrical cha

Question

13. After an electrical circuit component operates, there is some electrical charge remaining on the circuit. This is called the residual charge and it varies evenly between 50 and 110 Coulombs. Let E represent the residual charge on the electronic circuit component.

a) Find the probability the residual charge is at most 84 Coulombs. What distribution and parameters are you using? (5 points)

b) Given that the residual charge is between 62 and 75 Coulombs, find the probability it is less than 68. (4 points)

c) Only 14% of residual charges in this electrical circuit component are higher than y Coulombs. Calculate y. (4 points)

Explanation / Answer

Ans:

From this we can find the mean value of the residual charge= 50+110/2= 80

The standard deviation of the residual component= 30

From the Z conversion, we find that Z= 84-80/30= 0.133

Thus, p(E<=84)= p(Z<=0.133)= 0.5+0.0517= 0.5517

The distribution is normal converted into standard normal for calculation purposes.

= p( 62<E<68)= p(-0.6<Z<-0.4)= .2257-0.1554= 0.0703

From the Z tables, we find that this happens when Z value of the corresponding y is 1.08

Thus, 1.08=y-80/30

Then, y=112.4

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