The table on the right gives the annual income for eight families, in thousands of dollars. Find the number of standard deviations family H's income is from the mean. Income $\begin{array}{lllllllll}45 & 47 & 46 & 44 & 43 & 44 & 41 & 42\end{array}$

Step 1 ：First, we need to calculate the mean (average) of the incomes. The mean is calculated by adding up all the numbers and then dividing by the count of the numbers.

Step 2 ：We have the incomes as \([45, 47, 46, 44, 43, 44, 41, 42]\). Adding these up and dividing by 8, we get the mean income as \(44.0\) thousand dollars.

Step 3 ：Next, we need to calculate the standard deviation. The standard deviation is a measure of how spread out the numbers are from the mean. It is calculated by taking the square root of the variance. The variance is the average of the squared differences from the mean.

Step 4 ：Calculating the standard deviation for the given incomes, we get the standard deviation as approximately \(1.87\).

Step 5 ：Finally, we need to find how many standard deviations family H's income is from the mean. This is calculated by subtracting the mean from family H's income and then dividing by the standard deviation.

Step 6 ：Family H's income is \(42\) thousand dollars. Subtracting the mean income from this and dividing by the standard deviation, we get approximately \(-1.07\).

Step 7 ：Final Answer: Family H's income is approximately \(\boxed{-1.07}\) standard deviations from the mean.