Worked out steps to answer A.) 25points-5 points each wood products remanufactur

Question

Worked out steps to answer A.)

25points-5 points each wood products remanufacturer produces 4 sizes of moulding in the following proportions: 24 mm 32 mm 40 mm 48 mm 25% 35% 10% 30% Assume the following pieces greater or equal to 40 mm are considered large, while pieces less than 40 mm are considered small; all sampling is done with replacement. a) Calculate standard deviation of moulding size. b) If 8 pieces of moulding are randomly selected, what is the probability of getting exactly two pieces of each of the four sizes? c) What is the probability of not selecting a large piece? d) What is the probability of not selecting a large piece in a sample of 8? e) If 5% of the pieces are defective, what is the probability of producing an hcceptable piece or a large piece? Answor Lays 69.2865 (6) 36 o, o (d) 0.0168

Explanation / Answer

a)

b)

from multinomial distrbution selecting 2 of ech type =(8!/(2!*2!*2!*2!))*(0.25)2*(0.35)2*(0.1)2*(0.3)2 =0.01736

c)

P(not selecting a larger pieice =P(selecting a size less than 40 mm) =0.25+0.35 =0.6

d)

probabilty =P(all 8 are smaller than 40)=(0.6)8 =0.0168

e) probabilit =1-P(less than 40 and defective) =1-0.6*0.05=0.97

x p(x) xP(x) (x-)2 (x-)2P(x) 24 0.250 6.000 134.560 33.640 32 0.350 11.200 12.960 4.536 40 0.100 4.000 19.360 1.936 48 0.300 14.400 153.760 46.128 total 1 = 35.60 320.640 2= 86.2400 std deviation=     =    2 = 9.2865

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