015 Wawasan Engineering Bhd produces wine bottle corks. Currently, the company u

Question

015 Wawasan Engineering Bhd produces wine bottle corks. Currently, the company uses machines from PTL International to cut the bottle corks. The diameter of bottle corks, X is modelled as Gaussian random variable. Details of the diameter of bottle cork are presented in below. Diameter (cm) X S 2.92 X 2 3.16 Percentage 20% 5% (a) Calculate the average diameter, 14x, and standard deviation· Ox, of bottle cork, X. (b) Calculate the probability that the diameter of the bottle cork is within two standard deviation (c) Acceptable range of diameter of bottle cork, Xis (d) Wawasan Engineering is considering to purchase cork cutting machines from Taiwan Note : Round the values of x and x to I decimal point. of its mean value. Suggest the value a that would 95% of the bottle corks are within the acceptable range. Engineering Int to replace the current machines. The machine produces corks with diameters that have Gaussian distribution with mean 3.04cm and standard deviation 0.2cm. Should Wawasan Engineering purchase the machines from Taiwan Engineering Int. if the com decided that the diameter of acceptable corks must be between 2.85 cm and 3.15 cm? pany

Explanation / Answer

P(X < 2.92) = 0.20

P(Z < z*) = 0.20
z* = -0.841
(2.92 - mean)/sd = -0.841

P(X > 3.16) = 0.05
P(Z > z*) = 0.05
z* = 1.645

(3.16 - mean)/sd = 1.645

solving both equation
we get
mean = 93262/31075 =3.00119
sd = 120/1243 = 0.09654

b)
P(-2 <Z <2) = 0.9545
c)
P(-z <Z< z) = 0.95
z = 1.96
a = z *sd
= 1.96 * 0.09654 = 0.1892184

d)
3.04 - 2 * 0.2 = 3.04 - 0.4 = 2.64
3.04 + 2 *0.2 = 3.04 + 0.4 = 3.44
(2.64,3.44)
required - (2.85,3.15)

since 2.85 > 2.64
hence
Wawasan Engineering should not apurchase from Taiwan Engineering Int.)

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