Question

A machine produces parts with lengths that are normally distributed with σ = 0.55. A sample of 20 parts has a mean length of 76.47.

(a) Give a point estimate for μ. (Give your answer correct to two decimal places.)


(b) Find the 90% confidence maximum error of estimate for μ. (Give your answer correct to three decimal places.)


(c) Find the 90% confidence interval for μ. (Give your answer correct to three decimal places.)

Lower Limit -

Upper Limit -

d) How large a sample should be taken if the population mean is to be estimated with 99% confidence to within $83? The population has a standard deviation of $893. (Round your answer up to the next whole number.)

Answer 1

Ans:

a)

Point estimate=76.47

b)

Margin of error or maximum error of estimate=1.645*(0.55/sqrt(20))=0.202

c)

Lower limit=76.47-0.202=76.268

Upper limit=76.47+0.202=76.672

d)

Sample size required,n=(2.576*893/83)^2=769