Refer to Exercise 5.26 but suppose that a large potential contract contains the specification that at most \(7.5 \%\) can have a flow coefficient less than \(420 \mathrm{C}_{\mathrm{v}}\). If the manufacturing process is improved to meet this specification, determine

(a) the new mean \(\mu\) if the standard deviation is \(25 \mathrm{C}_{\mathrm{v}}\);

(b) the new standard deviation if the mean is \(496 \mathrm{C}_{\mathrm{v}}\).

Data From Exercise 5.26

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5.26 Butterfly-style valves used in heating and ventilat- ing industries have a high flow coefficient. Flow co- efficient can be modeled by a normal distribution with mean 496 C, and standard deviation 25 Cy. Find the probability that a valve will have a flow coefficient of (a) at least 450 Cv; (b) between 445.5 and 522 Cv.