To solve this problem we will apply the normal distribution, with which we will obtain the probability that the given event will occur. Concepts such as the mean and standard deviation will be present throughout the solution of the problem. Increasing or decreasing the average would change the location or center point of the curve. The change in the standard deviation would lead to the change in the dispersion of the data. As the standard deviation increases, the curve would become flatter.
Let X be the output voltage of power supply
X∼N [tex](5,0.02^2)[/tex]
A
The lower and upper specifications for voltage are 4.95 V and 5.05 V, respectively
[tex]P(4.95<X<5.05)=P(X<5.05)-P(X<4.95)[/tex]
[tex]P(4.95<X<5.05) =P(X-\mu \sigma<5.05-50.02)-P(X-\mu \sigma<4.95-50.02)[/tex]
[tex]P(4.95<X<5.05)=P(Z<2.5)-P(Z<-2.5)[/tex]
[tex]P(4.95<X<5.05)=0.99379-0.00621[/tex]
[tex]P(4.95<X<5.05)=0.9876[/tex]
Hence probability that a power supply selected at random will conform to the specifications on voltage is 0.9876
