The defect length of a corrosion defect in a pressurized steel pipe is normally

Question

The defect length of a corrosion defect in a pressurized steel pipe is normally distributed with mean value 28 mm and standard deviation 7.4 mm. (a) What is the probability that defect length is at most 20 mm? Less than 20 mm? (Round your answers to four decimal places.) at most 20mm 14007 less than 20mm 14007 b) what is the 75th percentile of the defect length distribution that is the value that separates the smallest 7 % of a engths from the largest 25%? Round your ans e tot ee decimal places. (c) What is the 15th percentile of the defect length distribution? (Round your answer to three decimal places.) (d what values separate the middle 80% of the defect length distribution from the smallest 10% and the largest 109? Round your answers to tree e-ma paces smallest 10% largest 10% You may need to use the appropriate table in the Appendix of Tables to answer this question

Explanation / Answer

b) for 75th percentile ; z score =0.67

hence corresponding value =28+0.67*7.4 =32.958

c)

for 15 th percentile ; z score =-1.03

corresponding value =28-1.03*7.4 =20.378

d)

for smallest 10% =  28-1.28*7.4 =18.528

largest 10% =  28+1.28*7.4 =37.472

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