Consider a normal population distribution with the value of

Consider a normal population distribution with the value of sigma known. What is the confidence level for the interval x plusminus 2.81 sigma / squareroot n? (Round your answer to one decimal place.) What is the confidence level for the Interval x plusminus 1.48 sigma/ squareroot n ? (Round your answer to one decimal place.)

Solution

as the problem said that is normal distribution and we know the value of sigma of population we will use Z distribution table to find the confidence interval

a)

for 2.81   probability = 0.00248

alpha / 2 = 0.00248

alpha = 0.00496

confidence interval = 1 - 0.00496 = 0.99504 = 99.5%

b)

for 1.48    probability = 0.0694

alpha / 2 = 0.0694

alpha = 0.1388

confidence interval = 1 - 0.1388 = 0.8612 = 86.12%