The life of a particular brand of television picture tube is known to be normall

Question

The life of a particular brand of television picture tube is known to be normally distributed with a standard deviation of 400 hours. Suppose that a random sample of 20 tubes resulted in an average lifetime of 9000 hours.

part1 - Obtain a 90% confidence interval estimate of the mean lifetime of such a tube.
part 2 - What is the possible size of the error?
part 3 - Obtain a 95% confidence interval estimate and possible error.
part 4 - Possible errors in 90% and 95% confidence intervals, increase or decrease. Why?

Not savvy with confidence intervals. Any help?

Explanation / Answer

here mean=9000, sd=400 and sample size=n=20,

(1-alpha)*100% confidence interval for mean=mean± z(alpha/2)*sd/sqrt(n)

(part1)90% confidence interval for mean=9000±z(0.1/2)*400/sqrt(20)=9000±1.645*400/sqrt(20)=

9000±147.13=(8852.87,9147.13)

(part2)possible error=147.13 for 90% confidence interval

(part3)95% confidence interval for mean=9000±z(0.05/2)*400/sqrt(20)=9000±1.96*400/sqrt(20)=

9000±175.31=(8824.61,9175.31)

(part4)possible error=175.31 for 95% confidence interval, increases from 90% confidence interval

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