A recent survey of 252 customers, selected at random from a database with 12,861 customers, found that 208 are satisfied with the service they are receiving. Find the upper bound of a 99% confidence interval for the percentage satisfied for all customers in the database.

The upper bound of a 99% confidence interval for the percentage satisfied for all customers in the database is 88.70%.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.

In which

z is the zscore that has a pvalue of .

Sample of 252 customers, 208 are satisfied:

This means that

99% confidence level

So , z is the value of Z that has a pvalue of , so .

The upper limit of this interval is:

As a percentage:

100%*0.8870 = 88.70%

The upper bound of a 99% confidence interval for the percentage satisfied for all customers in the database is 88.70%.

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