Final answer:
The 95% confidence interval for the mean number of daily calls received by the call center, based on the sample data, is approximately (155.69, 176.71).
Step-by-step explanation:
To find the 95% confidence interval for the mean number of daily calls received by the call center, we will use the formula for a confidence interval for a population mean when the population standard deviation is unknown:
Confidence Interval = ºr{x} ± (t* × (s / √n))
- ºr{x} is the sample mean.
- t* is the t-score that corresponds to the desired level of confidence and degrees of freedom.
- s is the sample standard deviation.
- n is the sample size.
Given:
ºr{x} = 166.2,
s = 22.8, and
n = 21.
Since we do not know the population standard deviation, we will use the t-distribution. For a 95% confidence interval and 20 degrees of freedom (n-1 = 21-1), the t-score is approximately 2.086 (from the t-distribution table or a calculator).
Calculating the margin of error:
Margin of Error = t* × (s / √n) = 2.086 × (22.8 / √21) ≈ 10.51
Therefore, the 95% confidence interval for the mean number of daily calls is:
166.2 ± 10.51 = (155.69, 176.71)
The travel agency can be 95% confident that the mean number of calls lies within this interval.