There are two machines available for cutting corks intended for use in wine bott

Question

There are two machines available for cutting corks intended for use in wine bottles. Measurements of 25 corks from the first machine indicates that it produces corks with diameters that are distributed with a sample mean 3.02 cm and sample standard deviation 0.07 cm. Measurements of 30 corks from the second machine reveals that it produces corks with diameters that have a distribution with sample mean 3.02 cm and sample standard deviation 0.04 cm. Acceptable corks have diameters between 2.9 cm and 3.1 cm. What is the uncertainty in the true mean cork diameter for the first machine? (Round your answer to four decimal places.) What is the uncertainty in the true mean cork diameter for the second machine? (Round your answer to four decimal places.) What is the probability that the first machine will produce an acceptable cork? (Round your answer to four decimal places.) what is the probability that the second machine will produce an acceptable cork? (Round your answer to four decimal places.)

Explanation / Answer

Ans:

a)For machine 1,uncertainity in true mean=0.07/sqrt(25)=0.0140

b)For machine 2,uncertainity in true mean=0.04/sqrt(30)=0.0073

c)For machine 1

z(2.9)=(2.9-3.02)/0.014=-8.5714

z(3.1)=(3.1-3.02)/0.014=5.7143

P(-8.5714<=z<=5.7143)=1-0=1

d)

z(2.9)=(2.9-3.02)/0.0073=-16.43

z(3.1)=(3.1-3.02)/0.0073=10.96

P(-16.43<=z<=10.96)=1-0=1

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