To calculate the 80% confidence interval for the population mean $\mu$, we will follow these steps:

Step 1: Calculate the sample mean

The sample data is: $550, 620, 710, 520, 480$

The sample mean $\bar{x}$ is calculated as:

$\bar{x} = \frac{550 + 620 + 710 + 520 + 480}{5} = \frac{2880}{5} = 576$

Step 2: Calculate the sample standard deviation

First, calculate the deviations from the mean, square them, and then find the average of these squared deviations (this is the variance).

$\text{Deviation} = x - \bar{x}$ $\text{Deviations} = 550 - 576, 620 - 576, 710 - 576, 520 - 576, 480 - 576$ $= -26, 44, 134, -56, -96$ Square these deviations: [ (-26)^2 = 676, \quad 44^2 = 1936, \quad 134^2 = 17956, \quad (-570^r12 - negativegence would . and teace21 is said