Suppose a random variable has population mean 140 and popula

Suppose a random variable has population mean -140 and population standard deviation 40. What is the upper value of the probability interval containing 95% of the sample means of sample size n = 100? (Round to 2 decimal places.)

Suppose a random variable has population standard deviation 25. What is the margin of error corresponding to the 95% confidence interval for sample a mean constructed from a sample of size 49? (Round to 2 decimal places.)

Solution

Given a=1-0.95=0.05, Z(0.05) = 1.645 (from standard normal table)

So the upper bound is

xbar + Z*s/vn = 140 -1.645*40/sqrt(100) = 133.42

----------------------------------------------------------------------------------------------------------

Given a=1-0.95= 0.05, Z(0.025) = 1.96 (from standard normal table)

So the margin of error = Z*s/vn = 1.96*25/sqrt(49) =7