Using Chebyshev's theorem, solve these problems for a distribution with a mean of 80 and a standard deviation of 16 . Round $k$ to at least 2 decimal places and final answers to at least one decimal place if needed.
Part 1 of 2
At least $\square \%$ of the values will fall between 32 and 128 .
Part 2 of 2
At least $\square \%$ of the values will fall between 37 and 123 .

Step 1 ：Given a distribution with a mean of 80 and a standard deviation of 16, we are asked to find the percentage of values that will fall within certain ranges according to Chebyshev's theorem.

Step 2 ：Chebyshev's theorem states that at least \(1 - 1/k^2\) of the data will fall within \(k\) standard deviations of the mean, where \(k\) is any real number greater than 1.

Step 3 ：For part 1, we are asked to find the percentage of values that will fall between 32 and 128. This range is 3 standard deviations away from the mean (48/16 = 3). So, we set \(k = 3\).

Step 4 ：Substituting \(k = 3\) into the formula, we get \(1 - 1/3^2 = 1 - 1/9 = 8/9 = 0.8889\). So, at least 88.9% of the values will fall between 32 and 128.

Step 5 ：For part 2, we are asked to find the percentage of values that will fall between 37 and 123. This range is 2.6875 standard deviations away from the mean (43/16 = 2.6875). So, we set \(k = 2.6875\).

Step 6 ：Substituting \(k = 2.6875\) into the formula, we get \(1 - 1/2.6875^2 = 1 - 1/7.2181 = 0.8615\). So, at least 86.2% of the values will fall between 37 and 123.

Step 7 ：Final Answer: \nPart 1: \(\boxed{88.9\%}\) of the values will fall between 32 and 128.\nPart 2: \(\boxed{86.2\%}\) of the values will fall between 37 and 123.