The brain volumes $\left(\mathrm{cm}^{3}\right.$ ) of 20 brains have a mean of $1131.2 \mathrm{~cm}^{3}$ and a standard deviation of $127.8 \mathrm{~cm}^{3}$. Use the given standard deviation and the range rule of thumb to identify the limits separating values that are significantly low or significantly high. For such data, would a brain volume of $1346.8 \mathrm{~cm}^{3}$ be significantly high? Significantly low values are $\square \mathrm{cm}^{3}$ or lower. (Type an integer or a decimal. Do not round.) Significantly high values are $\square \mathrm{cm}^{3}$ or higher. (Type an integer or a decimal. Do not round.)

Step 1 ：The mean brain volume is given as \(1131.2 \mathrm{cm}^{3}\) and the standard deviation is \(127.8 \mathrm{cm}^{3}\).

Step 2 ：The range rule of thumb states that most values should lie within 2 standard deviations of the mean. Therefore, we can calculate the limits for significantly low and high values by subtracting and adding 2 standard deviations from the mean, respectively.

Step 3 ：Calculating the lower limit: \(1131.2 - 2 \times 127.8 = 875.6 \mathrm{cm}^{3}\). So, significantly low values are \(875.6 \mathrm{cm}^{3}\) or lower.

Step 4 ：Calculating the upper limit: \(1131.2 + 2 \times 127.8 = 1386.8 \mathrm{cm}^{3}\). So, significantly high values are \(1386.8 \mathrm{cm}^{3}\) or higher.

Step 5 ：We are asked to determine if a brain volume of \(1346.8 \mathrm{cm}^{3}\) is significantly high. Comparing this value with the calculated limits, we find that \(1346.8 \mathrm{cm}^{3}\) is less than the upper limit of \(1386.8 \mathrm{cm}^{3}\).

Step 6 ：Final Answer: The limits for significantly low and high values are \(\boxed{875.6 \mathrm{~cm}^{3}}\) and \(\boxed{1386.8 \mathrm{~cm}^{3}}\), respectively. The given brain volume of \(1346.8 \mathrm{~cm}^{3}\) is not significantly high.