A machine produces parts with lengths that are normally distributed with displaystylesigma={0.66}. A sample of 20 parts has a mean length of 75.98. a)

zi2lalZ 2020-12-12 Answered
A machine produces parts with lengths that are normally distributed with σ=0.66. A sample of 20 parts has a mean length of 75.98.
a)
Give a point estimate for μ. (Give your answer correct to two decimal places.)
b)
Find the 95% confidence maximum error of estimate for μ. (Give your answer correct to two decimal places.)
c)
Find the 95% confidence interval for μ. (Give your answer correct to two decimal places.)
Lower limit =?
Upper limit =?
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Expert Answer

Cullen
Answered 2020-12-13 Author has 89 answers
Step 1
Given:
A machine produces parts with lengths that are normally distributed with σ=0.66. A sample of 20 parts has a mean length of 75.98.
To Determine:
a) A point estimate for μ.
b) The 95% confidence maximum error of estimate for μ.
c) The 95% confidence interval for μ
Step 2
Solution:
A machine produces parts with lengths that are normally distributed with the given values,
σ=0.66,n=20,x=75.98
a) A point estimate for μ is
μ=x=75.98
b) For 95% confidence intervals,
Z - critical value is 1.96.
So, The maximum confidence error of estimate for μ is,
M.E.=Z×σn
M.E.=1.96×0.6620
M.E.=1.96×0.664.4721
M.E.=1.29364.4721=0.289260
c) The 95% confidence interval for μ,
Lower Limit =xM.E.
L.L.,
=75.980.289260
=75.69074
Upper Limit =x+M.E.
U.L.,
=75.98+0.289260
=76.26926
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