Question

An Internet service provider sampled 540 customers and found that 75 of them had experienced an interruption in high-speed service during the previous month. Compute a 99% confidence interval for the proportion of customers who have experienced a service interruption during the previous month.

Answer 1

Solution :

Here , X be a customers that experienced an interuption in high speed service during the previous month

X = 75.

And number of internet service provider ( n ) = 540

Proportion of interuption in high-speed provider in previous month is

Formula of one sample proportion is :

where = 2.58 ......(standard normal table value for Z0.005 )

Now

Lower limit :

Also , Upper limit ;

Upper = 0.177

So 99% confidence interval for proportion of customer who have experienced a service interrution during the previous month is ( 0.101 , 0.177)