A machine that cuts corks for wine bottles operates in such a way that the distr

Question

A machine that cuts corks for wine bottles operates in such a way that the distribution of the diameter of the corks produced is well approximated by a normal distribution with mean 4 cm and standard deviation 0.2 cm. The specifications call for corks with diameters between 3.7 and 4.3 cm. A cork not meeting the specifications is considered defective. (A cork that is too small leaks and causes the wine to deteriorate; a cork that is too large doesn't fit in the bottle.) What proportion of corks produced by this machine are defective? (Round the answer to four decimal places.)

Explanation / Answer

given

mean 4 cm and

standard deviation 0.2 cm.

The specifications call for corks with diameters between 3.7 and 4.3 cm

X~N(4, 0.2)

Within spec, P{3.7<X<4.3}=P{z1<Z<z2},

where z1=(3.7-4)/0.2 = -1.5,

z2=(4.3-4)/0.2)=1.5

P=P{Z<z2}-P{Z<z1} =. 0.9332-0.0668 = 0.8664 we have the values from standard distribution table

not meeting specification = 1-0.8664 = 0.1336

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.