Final answer:
The range of the repair costs is $412,219 and the sample standard cost of the repair is $307,821.
Step-by-step explanation:
The range of repair costs can be found by subtracting the smallest cost from the largest cost. In this case, the smallest cost is $240 and the largest cost is $412,459. So, the range is $412,459 - $240 = $412,219.
To find the sample standard cost of the repair, we need to calculate the standard deviation. First, calculate the mean (average) of the repair costs. The mean is the sum of all the costs divided by the number of costs. In this case, there are four costs: $412,459, $405, and $240. So, the mean is ($412,459 + $405 + $240) / 4 = $137,368.
To calculate the standard deviation, subtract the mean from each cost, square the difference, sum the squared differences, divide by (n-1), and take the square root. In this case, the squared differences are: ($412,459 - $137,368)^2, ($405 - $137,368)^2, and ($240 - $137,368)^2. Summing the squared differences gives: ($275,091,091,264 + $107,995,298 + $8,923,926,464) = $284,010,315,726. Dividing by (n-1), where n is the number of costs (4-1), gives: $284,010,315,726 / 3 = $94,670,105,242. Taking the square root of this value gives the standard deviation: sqrt($94,670,105,242) = $307,821. Therefore, the sample standard cost of the repair is $307,821.