5.         WellingtonFabrics of New Zealand produces bolts of woolen cloth for export.Each bolt contains 30 yards of fabric. Industry standards call forthe average number of defects per fabric bolt to not exceed five.An inspector randomly selected a bolt of cloth, examined the first3 yards and found 3 defects therein. The company assumes that thedefect rate follows the Poisson distribution.

a.          Given theabove information, if the company is meeting the industrystandards, what is the average number of defects expected in a3-yard segment of a cloth bolt?

b.         Calculate theprobability of finding 3 or more defects in a 3-yard segment ofcloth given the above information.

c.          Given youranswer to part b., does it appear that the company is meeting theindustry standard for quality? Explain briefly.

d.         To verify thefindings the inspector examines 15 yards of another bolt of clothand discovers five defects.

i.          Calculatethe average number of defects expected in a 15-yard segment ofcloth;

ii.         Calculate theprobability of finding five or more defects in the 15-yard clothsegment.

e.          The normaldistribution can be used to approximate the Poisson distribution.To calculate a z-score you need the mean and standard deviation.Remember that the mean and variance of a Poisson random variableare equal.

i.          Calculatethe mean and standard deviation for the number of defects in a15-yard segment of cloth.

ii.         Use this meanand standard deviation to calculate the probability of finding fiveor more defects in a 15-yard segment of cloth using the normalapproximation. [Remember to use the continuity correction!]

iii.        How accurate is thisapproximation?