Question

There are two machines available for cutting corks intended for use in wine bottles. The first produces corks with diameters that are normally distributed with mean 3 cm and standard deviation 0.1cm. The second machine produces corks with diameters that have a normal distribution with mean 3.04 cm and standard deviation 0.02 cm. Acceptable corks have diameters between 2.9 and 3.1 cm.

(a)-What is the probability that the first machine produces an acceptable cork? (Round your answer to four decimal places.)
(b)-What is the probability that the second machine produces an acceptable cork? (Round your answer to four decimal places.)

Answer 1

Explanation:

Given that there are two machines available for cutting corks intended for use in wine bottles.

X1 = diameter of I machine and X2 = diameter of II machine

X1 is N(3.04, 0.02) and X2 is N(2.9, 3.1)

Acceptable is mean =3 and std dev = 0.1

a)
`P(2.9<x1<3.1)=P(|z|<10)\\=1.0000`

b)
`P(2.9<x1<3.1) =P((2.9-3.04)/(0.02)<Z<(2.9-3.04)/(0.02)) \\=P(|Z|<7) = 1.0000`

Both are certain events.