A customer’s specification for weight of an antiseptic cream sold in plastic tubes is 4.00 ounces ± 0.02 ounces. The target process capability ratio is 1.00. At Brooklyn Pharmaceuticals, the current distribution of the filling process is centered on 4.005 ounces with a standard deviation of 0.004 ounces. Compute Cp and Cpk and report whether the filling process is capable of delivering to customer specifications? Customer Specification 3.98
Process Average 4.005
Process Standard Deviation 0.004

Cp = 1.667

Cpk = 1.25

The filling process will deliver the customer's specifications since Cp > 1 and Cpk > 1

Explanation:

Given data:

Customer Specification           3.98          4.02

Process Average                      4.005

Process Standard Deviation    0.004

Calculate the Cp and Cpk values

Cp = Δ customer specification / ( 6 * std )

     = (4.02 - 3.98 ) / ( 6 * 0.04 )

     = 0.04 / 0.24 = 0.1667 + 1 = 1.667

Cpk ( upper ) = ( 4.02 - process average ) / ( 3* std )

                      = ( 4.02 - 4.005 ) / ( 3 * 0.004 )  = 1.25

Cpk ( lower ) = ( process average - 3.98 ) / ( 3 * std )

                     = ( 4.005 - 3.98 ) / ( 3 * 0.04 ) = 2.083

Cpk = minimum value of Cpk = 1.25

start by isolating the variable on one side by adding 43w^2 to both sides.   the equation will read:

25w^2+5=0

*subtract 5 from both sides*

25w^2=-5

*divide both sides by 25*

w^2=-1/5

*take the square root of both sides*

w=√(-1/5)

the square root of -1 is i.   the square root of 5 remains √5

the answer is i/√5.

hope this