Question

An Army official wants to estimate the mean weight of a particular type of weapon. He takes a random sample of 100 weapons of this type and finds the sample mean is 48.1 lbs. and from the past military records he knows the population standard deviation is 0.12 lbs. Calculate a 98 percent confidence interval for the population mean.

Answer 1

Sample size = n = 100

Sample mean = = 48.1

Population standard deviation = = 0.12

We have to construct 98% confidenc interval for the population mean.

Here population standard deviation is known so we have to use one sample z-confidence interval.

z confidence interval

Here E is a margin of error

Zc = 2.32 ( Using z table)

So confidence interval is ( 48.1 - 0.0278 , 48.1 + 0.0278) = > ( 48.0722 , 48.1278)